Flavio Mercati | Perimeter Institute for Theoretical Physics (original) (raw)

Papers by Flavio Mercati

Physical Review D, 2011

Locality of interactions is an essential ingredient of Special Relativity. Recently, a new framew... more Locality of interactions is an essential ingredient of Special Relativity. Recently, a new framework under the name of relative locality has been proposed as a way to consider Planckian modifications of the relativistic dynamics of particles. We note in this paper that the loss of absolute locality is a general feature of theories beyond Special Relativity with an implementation of a relativity principle. We give an explicit construction of such an implementation and compare it both with the previously mentioned framework of relative locality and the so-

Physical Review D, 2012

In the context of departures from Special Relativity written as a momentum power expansion in the... more In the context of departures from Special Relativity written as a momentum power expansion in the inverse of an ultraviolet energy scale M , we derive the constraints that the relativity principle imposes between coefficients of a deformed (but rotational invariant) composition law, dispersion relation, and transformation laws, at first order in the power expansion. In particular, we find that, at that order, the consistency of a modification of the energy-momentum composition law fixes the modification in the dispersion relation. We therefore obtain the most generic modification of Special Relativity which is rotational invariant and that preserves the relativity principle at leading order in 1/M . * Electronic address: jcarmona@unizar.es, cortes@unizar.es, flavio.mercati@gmail.com 1 This is an heuristic argument that is explicitly seen in the constraints one gets for rotational and nonrotational invariant parameters in the SME, see e.g. . Up to our knowledge there are no such type of studies in the case of a deformed symmetry, but considering a rotational invariant deformation is a common practice in DSR theories and will prove to be an important algebraic simplification in the analysis presented here.

Physical Review D, 2011

Locality of interactions is an essential ingredient of Special Relativity. Recently, a new framew... more Locality of interactions is an essential ingredient of Special Relativity. Recently, a new framework under the name of relative locality [G. Amelino-Camelia, L. Freidel, J. Kowalski-Glikman, and L. Smolin, arXiv:1101.0931.] has been proposed as a way to consider Planckian modifications of the relativistic dynamics of particles. We note in this paper that the loss of absolute locality is a general

The literature on quantum-gravity-inspired scenarios for the quantization of space–time has so fa... more The literature on quantum-gravity-inspired scenarios for the quantization of space–time has so far focused on particle-physics-like studies. This is partly justified by the present limitations of our understanding of quantum gravity theories, but we here argue that valuable insight can be gained through semi-heuristic analyses of the implications for gravitational phenomena of some results obtained in the quantum space–time literature.

We investigate the question whether small quantum-gravitational effects can be observed in the an... more We investigate the question whether small quantum-gravitational effects can be observed in the anisotropy spectrum of the cosmic microwave background radiation. An observation of such an effect is needed in order to discriminate between different approaches to quantum gravity. Using canonical quantum gravity with the Wheeler–DeWitt equation, we find a suppression of power at large scales.

We present the star-product algebra of the κ-deformation of Minkowski space and the formulation o... more We present the star-product algebra of the κ-deformation of Minkowski space and the formulation of Poincaré covariant differential calculus. We use the tools to construct a twisted K-cycle over the algebra and twisted cyclic cocycle.

The research work reported in this thesis intends to contribute to the understanding of theories ... more The research work reported in this thesis intends to contribute to the understanding of theories constructed in noncommutative spacetimes, spacetimes whose coordinates satisfy commutation relations of the type [xµ, xν]= iΘµν (x), with a noncommutativity matrix Θµν which may be coordinate dependent. Such theories have attracted strong interest in the context of research attempting to apply the principles of quantum mechanics to the fundamental description of spacetime structure.

We offer a preliminary exploration of the two sides of the challenge provided by the recent OPERA... more We offer a preliminary exploration of the two sides of the challenge provided by the recent OPERA data on superluminal neutrinos. On one side we stress that some aspects of this result are puzzling even from the perspective of the wild quantum-gravity literature, where arguments in favor of the possibility of superluminal propagation have been presented, but not considering the possibility of such a sizeable effect for neutrinos of such low energies. We feel this must encourage particularly severe scrutiny of the OPERA result. On the other side, we notice that the OPERA result is reasonably consistent with µ-neutrino-speed data previously obtained at FERMILAB, reported in papers of 2007 and 1979. And it is intriguing that these FERMILAB79 and FER-MILAB07 results, when combined with the new OPERA result, in principle provide a window on µ-neutrino speeds at different energies broad enough to compare alternative phenomenological models. We test the discriminating power of such an approach by using as illustrative examples the case of special-relativistic tachyons, the case of "Coleman-Glashow-type" momentum-independent violations of the special-relativistic speed law, and the cases of linear and quadratic energy dependence of the speed of ultrarelativistic muon neutrinos. Even just using µ-neutrino data in the range from ∼ 3 GeVs to ∼ 200 GeVs the special-relativistic tachyon and the quadratic-dependence case are clearly disfavoured. The linear-dependence case gives a marginally consistent picture and the Coleman-Glashow scenario fits robustly the data. We also comment on Supernova 1987a and its relevance for consideration of other neutrino species, also in relation with some scenarios that appeared in the large-extra-dimension literature.

The reference laboratory bounds on superluminality of the electron are obtained from the absence ... more The reference laboratory bounds on superluminality of the electron are obtained from the absence of in-vacuo Cherenkov processes and the determinations of synchrotron radiated power for LEP electrons. It is usually assumed that these analyses establish the validity of a standard special-relativistic description of the electron with accuracy of at least a few parts in 10 14 , and in particular this is used to exclude electron superluminality with such an accuracy. We observe that these bounds rely crucially on the availability of a preferred frame. In-vacuo-Cherenkov processes are automatically forbidden in any theory with "deformed Lorentz symmetry", relativistic theories that, while different from Special Relativity, preserve the relativity of inertial frames. Determinations of the synchrotron radiated power can be used to constrain the possibility of Lorentz-symmetry deformation, but provide rather weak bounds, which in particular for electron superluminality we establish to afford us no more constraining power than for an accuracy of a few parts in 10 4 . We argue that this observation can have only a limited role in the ongoing effort of analysis of the anomaly tentatively reported by the OPERA collaboration, but we stress that it could provide a valuable case study for assessing the limitations of "indirect" tests of fundamental laws of physics.

Locality of interactions is an essential ingredient of Special Relativity. Recently, a new framew... more Locality of interactions is an essential ingredient of Special Relativity. Recently, a new framework under the name of relative locality has been proposed as a way to consider Planckian modifications of the relativistic dynamics of particles. We note in this paper that the loss of absolute locality is a general feature of theories beyond Special Relativity with an implementation of a relativity principle. We give an explicit construction of such an implementation and compare it both with the previously mentioned framework of relative locality and the so-

We explore the problem of time in quantum gravity in a point-particle analogue model of scale-inv... more We explore the problem of time in quantum gravity in a point-particle analogue model of scale-invariant gravity. If quantized after reduction to true degrees of freedom, it leads to a time-independent Schrödinger equation. As with the Wheeler-DeWitt equation, time disappears, and a frozen formalism that gives a static wavefunction on the space of possible shapes of the system is obtained. However, if one follows the Dirac procedure and quantizes by imposing constraints, the potential that ensures scale invariance gives rise to a conformal anomaly, and the scale invariance is broken. A behaviour closely analogous to renormalization-group (RG) flow results. The wavefunction acquires a dependence on the scale parameter of the RG flow. We interpret this as time evolution and obtain a novel solution of the problem of time in quantum gravity. We apply the general procedure to the three-body problem, showing how to fix a natural initial value condition, introducing the notion of complexity. We recover a time-dependent Schrödinger equation with a repulsive cosmological force in the 'late-time' physics and we analyse the role of the scale invariant Planck constant. We suggest that several mechanisms presented in this model could be exploited in more general contexts. * This work has been submitted in partial fulfillment of the Master Degree in Physics at the University of Pavia.

In the context of departures from Special Relativity written as a momentum power expansion in the... more In the context of departures from Special Relativity written as a momentum power expansion in the inverse of an ultraviolet energy scale M , we derive the constraints that the relativity principle imposes between coefficients of a deformed (but rotational invariant) composition law, dispersion relation, and transformation laws, at first order in the power expansion. In particular, we find that, at that order, the consistency of a modification of the energy-momentum composition law fixes the modification in the dispersion relation. We therefore obtain the most generic modification of Special Relativity which is rotational invariant and that preserves the relativity principle at leading order in 1/M . * Electronic address: jcarmona@unizar.es, cortes@unizar.es, flavio.mercati@gmail.com 1 This is an heuristic argument that is explicitly seen in the constraints one gets for rotational and nonrotational invariant parameters in the SME, see e.g. . Up to our knowledge there are no such type of studies in the case of a deformed symmetry, but considering a rotational invariant deformation is a common practice in DSR theories and will prove to be an important algebraic simplification in the analysis presented here.

We modify the Chandrasekhar model of white dwarfs by introducing novel momentum-space features th... more We modify the Chandrasekhar model of white dwarfs by introducing novel momentum-space features that characterize the analysis of some quantum-spacetime scenarios. We find that the rather standard ultraviolet effects of spacetime quantization can only be significant in a regime where the Chandrasekhar model anyway lacks any contact with observations. But a new class of quantum-spacetime effects inspired by the mechanism of "ultraviolet/infrared mixing" could be relevant for white dwarfs whose mass is roughly half the mass of the Sun, some of which are described in the literature as "strange white dwarfs". We also offer a preliminary argument suggesting that Planck-scale (ultraviolet) effects could be significant in cases where ultra-high densities are present, even when the relevant star is still gigantic in Planck-length units. arXiv:0906.2016v2 [gr-qc]

We show that there are 2 equivalent first order descriptions of 2 + 1 gravity with non-zero cosmo... more We show that there are 2 equivalent first order descriptions of 2 + 1 gravity with non-zero cosmological constant. One is the well-known spacetime description and the other is in terms of evolving conformal geometry. The key tool that links these pictures is Cartan geometry, a generalization of Riemannian geometry that allows for geometries locally modeled off arbitrary homogeneous spaces. The two different interpretations suggest two distinct phase space reductions.

We show that the κ-Poincaré Hopf algebra can be interpreted in the framework of curved momentum s... more We show that the κ-Poincaré Hopf algebra can be interpreted in the framework of curved momentum space leading to the relativity of locality [1]. We study the geometric properties of the momentum space described by κ-Poincaré, and derive the consequences for particles propagation and energy-momentum conservation laws in interaction vertices, obtaining for the first time a coherent and fully workable model of the deformed relativistic kinematics implied by κ-Poincaré. We describe the action of boost transformations on multi-particles systems, showing that in order to keep covariant the composed momenta it is necessary to introduce a dependence of the rapidity parameter on the particles momenta themselves. Finally, we show that this particular form of the boost transformations keeps the validity of the relativity principle, demonstrating the invariance of the equations of motion under boost transformations. arXiv:1106.5710v1 [gr-qc]

I introduce in κ-Minkowski noncommutative spacetime the basic tools of quantum differential geome... more I introduce in κ-Minkowski noncommutative spacetime the basic tools of quantum differential geometry, namely bicovariant differential calculus, Lie and inner derivatives, the integral, the Hodge- * and the metric. I show the relevance of these tools for field theory with an application to complex scalar field, for which I am able to identify a vector-valued four-form which generalizes the energy-momentum tensor. Its closedness is proved, expressing in a covariant form the conservation of energy-momentum.

Arxiv preprint arXiv:1106.0261, Jan 1, 2011

We question the emergence of a minimal length in quantum spacetime, confronting two notions that ... more We question the emergence of a minimal length in quantum spacetime, confronting two notions that appeared at various points in the literature: length as the spectrum of an operator L in the Doplicher Fredenhagen Roberts (DFR) quantum spacetime and the canonical noncommutative spacetime (θ-Minkowski) on the one side; Connes spectral distance in noncommutative geometry on the other side. Although on the Euclidean space -as well as on manifolds with suitable symmetry -the two notions merge into the one of geodesic distance, they yield distinct results in the noncommutative framework. In particular, the widespread idea that quantizing the coordinates inevitably yields a minimal length should be handle with care: on the Moyal plane for instance, both the quantum length d L (intended as the mean value of the length operator on a separable two-point state) and the spectral distance d D are discrete, but only the former is bounded above from zero. We propose a framework in which the comparison of d L with d D makes sense: by doubling the spectral triple, one turns the quantum length into a true distance function and, simultaneously, emphasises the "quantum mechanics flavor" of the spectral distance. Specifically, for any couple of identical states, d L is identified with the spectral distance on a two-sheet model (each state living on a distinct sheet). Using Pythagoras-like relations for spectral triples, we extend the identification to any couples of distinct states, provided the spectral distance d E on a single sheet coincides with a new distance d L induced by the length operator. This condition is not fulfilled on the Moyal plane. We interpret the discrepancy between d L and d E (which becomes negligible at high energy) as two distinct ways of integrating the line element on a quantum space. This leads us to propose an equation for a geodesic on the Moyal plane. * Pierre.Martinetti@roma1.infn.it † Flavio.Mercati@roma1.infn.it ‡ tomassini@sci.unich.it arXiv:1106.0261v1 [math-ph] 1 Jun 2011 * * Details on how a covariant Dirac operator modifies the metric can be found in e.g. [20] † † Notice that in the DFR model the quantum length between a state and itself constantly equals dL(ψ0, ψ0) (and is in fact minimum) if one considers only coherent states. Unfortunately dD between coherent states is still unknown, which forbids any comparison. This will be the subject of a future work.

Arxiv preprint arXiv:1106.5710, Jan 1, 2011

We show that the κ-Poincaré Hopf algebra can be interpreted in the framework of curved momentum s... more We show that the κ-Poincaré Hopf algebra can be interpreted in the framework of curved momentum space leading to the relativity of locality [1]. We study the geometric properties of the momentum space described by κ-Poincaré, and derive the consequences for particles propagation and energy-momentum conservation laws in interaction vertices, obtaining for the first time a coherent and fully workable model of the deformed relativistic kinematics implied by κ-Poincaré. We describe the action of boost transformations on multi-particles systems, showing that in order to keep covariant the composed momenta it is necessary to introduce a dependence of the rapidity parameter on the particles momenta themselves. Finally, we show that this particular form of the boost transformations keeps the validity of the relativity principle, demonstrating the invariance of the equations of motion under boost transformations. arXiv:1106.5710v1 [gr-qc]

… Field Theories: Pescara, Italy, 3-8 …, Jan 1, 2008

We consider some alternative scenarios for the fate of Poincaré/Lorentz symmetry at the Planck sc... more We consider some alternative scenarios for the fate of Poincaré/Lorentz symmetry at the Planck scale, and we discuss some opportunities to test these scenarios.

Arxiv preprint arXiv:1004.3352, Jan 1, 2010

We advocate a novel perspective on the phenomenology of a framework with spacetime noncommutativi... more We advocate a novel perspective on the phenomenology of a framework with spacetime noncommutativity which is of established relevance for string theory. Our analysis applies to cases in which the noncommutativity parameters are arranged according to the criteria of "light-like noncommutativity" and ultraviolet supersymmetry is assumed, so that the implications of the characteristic mechanism of ultraviolet/infrared mixing are relatively soft. We also observe that an analogous case of soft ultraviolet-infrared mixing is present in a previously-proposed Loop-quantum-gravity-inspired description of quantum spacetime. And we show that soft ultraviolet-infrared mixing produces an anomaly for the nonrelativistic de Broglie relation λv = h/m, with correction term governed by a single (but particle-dependent) parameter χ. We test this hypothesis by comparing a determination of the fine structure constant that relies on the de Broglie relation for nonrelativistic neutrons to other independent determinations of the fine structure constant, and we obtain an estimate of χ that differs from 0 with four-standard-deviation significance.

Physical Review D, 2011

Locality of interactions is an essential ingredient of Special Relativity. Recently, a new framew... more Locality of interactions is an essential ingredient of Special Relativity. Recently, a new framework under the name of relative locality has been proposed as a way to consider Planckian modifications of the relativistic dynamics of particles. We note in this paper that the loss of absolute locality is a general feature of theories beyond Special Relativity with an implementation of a relativity principle. We give an explicit construction of such an implementation and compare it both with the previously mentioned framework of relative locality and the so-

Physical Review D, 2012

In the context of departures from Special Relativity written as a momentum power expansion in the... more In the context of departures from Special Relativity written as a momentum power expansion in the inverse of an ultraviolet energy scale M , we derive the constraints that the relativity principle imposes between coefficients of a deformed (but rotational invariant) composition law, dispersion relation, and transformation laws, at first order in the power expansion. In particular, we find that, at that order, the consistency of a modification of the energy-momentum composition law fixes the modification in the dispersion relation. We therefore obtain the most generic modification of Special Relativity which is rotational invariant and that preserves the relativity principle at leading order in 1/M . * Electronic address: jcarmona@unizar.es, cortes@unizar.es, flavio.mercati@gmail.com 1 This is an heuristic argument that is explicitly seen in the constraints one gets for rotational and nonrotational invariant parameters in the SME, see e.g. . Up to our knowledge there are no such type of studies in the case of a deformed symmetry, but considering a rotational invariant deformation is a common practice in DSR theories and will prove to be an important algebraic simplification in the analysis presented here.

Physical Review D, 2011

Locality of interactions is an essential ingredient of Special Relativity. Recently, a new framew... more Locality of interactions is an essential ingredient of Special Relativity. Recently, a new framework under the name of relative locality [G. Amelino-Camelia, L. Freidel, J. Kowalski-Glikman, and L. Smolin, arXiv:1101.0931.] has been proposed as a way to consider Planckian modifications of the relativistic dynamics of particles. We note in this paper that the loss of absolute locality is a general

The literature on quantum-gravity-inspired scenarios for the quantization of space–time has so fa... more The literature on quantum-gravity-inspired scenarios for the quantization of space–time has so far focused on particle-physics-like studies. This is partly justified by the present limitations of our understanding of quantum gravity theories, but we here argue that valuable insight can be gained through semi-heuristic analyses of the implications for gravitational phenomena of some results obtained in the quantum space–time literature.

We investigate the question whether small quantum-gravitational effects can be observed in the an... more We investigate the question whether small quantum-gravitational effects can be observed in the anisotropy spectrum of the cosmic microwave background radiation. An observation of such an effect is needed in order to discriminate between different approaches to quantum gravity. Using canonical quantum gravity with the Wheeler–DeWitt equation, we find a suppression of power at large scales.

We present the star-product algebra of the κ-deformation of Minkowski space and the formulation o... more We present the star-product algebra of the κ-deformation of Minkowski space and the formulation of Poincaré covariant differential calculus. We use the tools to construct a twisted K-cycle over the algebra and twisted cyclic cocycle.

The research work reported in this thesis intends to contribute to the understanding of theories ... more The research work reported in this thesis intends to contribute to the understanding of theories constructed in noncommutative spacetimes, spacetimes whose coordinates satisfy commutation relations of the type [xµ, xν]= iΘµν (x), with a noncommutativity matrix Θµν which may be coordinate dependent. Such theories have attracted strong interest in the context of research attempting to apply the principles of quantum mechanics to the fundamental description of spacetime structure.

We offer a preliminary exploration of the two sides of the challenge provided by the recent OPERA... more We offer a preliminary exploration of the two sides of the challenge provided by the recent OPERA data on superluminal neutrinos. On one side we stress that some aspects of this result are puzzling even from the perspective of the wild quantum-gravity literature, where arguments in favor of the possibility of superluminal propagation have been presented, but not considering the possibility of such a sizeable effect for neutrinos of such low energies. We feel this must encourage particularly severe scrutiny of the OPERA result. On the other side, we notice that the OPERA result is reasonably consistent with µ-neutrino-speed data previously obtained at FERMILAB, reported in papers of 2007 and 1979. And it is intriguing that these FERMILAB79 and FER-MILAB07 results, when combined with the new OPERA result, in principle provide a window on µ-neutrino speeds at different energies broad enough to compare alternative phenomenological models. We test the discriminating power of such an approach by using as illustrative examples the case of special-relativistic tachyons, the case of "Coleman-Glashow-type" momentum-independent violations of the special-relativistic speed law, and the cases of linear and quadratic energy dependence of the speed of ultrarelativistic muon neutrinos. Even just using µ-neutrino data in the range from ∼ 3 GeVs to ∼ 200 GeVs the special-relativistic tachyon and the quadratic-dependence case are clearly disfavoured. The linear-dependence case gives a marginally consistent picture and the Coleman-Glashow scenario fits robustly the data. We also comment on Supernova 1987a and its relevance for consideration of other neutrino species, also in relation with some scenarios that appeared in the large-extra-dimension literature.

The reference laboratory bounds on superluminality of the electron are obtained from the absence ... more The reference laboratory bounds on superluminality of the electron are obtained from the absence of in-vacuo Cherenkov processes and the determinations of synchrotron radiated power for LEP electrons. It is usually assumed that these analyses establish the validity of a standard special-relativistic description of the electron with accuracy of at least a few parts in 10 14 , and in particular this is used to exclude electron superluminality with such an accuracy. We observe that these bounds rely crucially on the availability of a preferred frame. In-vacuo-Cherenkov processes are automatically forbidden in any theory with "deformed Lorentz symmetry", relativistic theories that, while different from Special Relativity, preserve the relativity of inertial frames. Determinations of the synchrotron radiated power can be used to constrain the possibility of Lorentz-symmetry deformation, but provide rather weak bounds, which in particular for electron superluminality we establish to afford us no more constraining power than for an accuracy of a few parts in 10 4 . We argue that this observation can have only a limited role in the ongoing effort of analysis of the anomaly tentatively reported by the OPERA collaboration, but we stress that it could provide a valuable case study for assessing the limitations of "indirect" tests of fundamental laws of physics.

Locality of interactions is an essential ingredient of Special Relativity. Recently, a new framew... more Locality of interactions is an essential ingredient of Special Relativity. Recently, a new framework under the name of relative locality has been proposed as a way to consider Planckian modifications of the relativistic dynamics of particles. We note in this paper that the loss of absolute locality is a general feature of theories beyond Special Relativity with an implementation of a relativity principle. We give an explicit construction of such an implementation and compare it both with the previously mentioned framework of relative locality and the so-

We explore the problem of time in quantum gravity in a point-particle analogue model of scale-inv... more We explore the problem of time in quantum gravity in a point-particle analogue model of scale-invariant gravity. If quantized after reduction to true degrees of freedom, it leads to a time-independent Schrödinger equation. As with the Wheeler-DeWitt equation, time disappears, and a frozen formalism that gives a static wavefunction on the space of possible shapes of the system is obtained. However, if one follows the Dirac procedure and quantizes by imposing constraints, the potential that ensures scale invariance gives rise to a conformal anomaly, and the scale invariance is broken. A behaviour closely analogous to renormalization-group (RG) flow results. The wavefunction acquires a dependence on the scale parameter of the RG flow. We interpret this as time evolution and obtain a novel solution of the problem of time in quantum gravity. We apply the general procedure to the three-body problem, showing how to fix a natural initial value condition, introducing the notion of complexity. We recover a time-dependent Schrödinger equation with a repulsive cosmological force in the 'late-time' physics and we analyse the role of the scale invariant Planck constant. We suggest that several mechanisms presented in this model could be exploited in more general contexts. * This work has been submitted in partial fulfillment of the Master Degree in Physics at the University of Pavia.

In the context of departures from Special Relativity written as a momentum power expansion in the... more In the context of departures from Special Relativity written as a momentum power expansion in the inverse of an ultraviolet energy scale M , we derive the constraints that the relativity principle imposes between coefficients of a deformed (but rotational invariant) composition law, dispersion relation, and transformation laws, at first order in the power expansion. In particular, we find that, at that order, the consistency of a modification of the energy-momentum composition law fixes the modification in the dispersion relation. We therefore obtain the most generic modification of Special Relativity which is rotational invariant and that preserves the relativity principle at leading order in 1/M . * Electronic address: jcarmona@unizar.es, cortes@unizar.es, flavio.mercati@gmail.com 1 This is an heuristic argument that is explicitly seen in the constraints one gets for rotational and nonrotational invariant parameters in the SME, see e.g. . Up to our knowledge there are no such type of studies in the case of a deformed symmetry, but considering a rotational invariant deformation is a common practice in DSR theories and will prove to be an important algebraic simplification in the analysis presented here.

We modify the Chandrasekhar model of white dwarfs by introducing novel momentum-space features th... more We modify the Chandrasekhar model of white dwarfs by introducing novel momentum-space features that characterize the analysis of some quantum-spacetime scenarios. We find that the rather standard ultraviolet effects of spacetime quantization can only be significant in a regime where the Chandrasekhar model anyway lacks any contact with observations. But a new class of quantum-spacetime effects inspired by the mechanism of "ultraviolet/infrared mixing" could be relevant for white dwarfs whose mass is roughly half the mass of the Sun, some of which are described in the literature as "strange white dwarfs". We also offer a preliminary argument suggesting that Planck-scale (ultraviolet) effects could be significant in cases where ultra-high densities are present, even when the relevant star is still gigantic in Planck-length units. arXiv:0906.2016v2 [gr-qc]

We show that there are 2 equivalent first order descriptions of 2 + 1 gravity with non-zero cosmo... more We show that there are 2 equivalent first order descriptions of 2 + 1 gravity with non-zero cosmological constant. One is the well-known spacetime description and the other is in terms of evolving conformal geometry. The key tool that links these pictures is Cartan geometry, a generalization of Riemannian geometry that allows for geometries locally modeled off arbitrary homogeneous spaces. The two different interpretations suggest two distinct phase space reductions.

We show that the κ-Poincaré Hopf algebra can be interpreted in the framework of curved momentum s... more We show that the κ-Poincaré Hopf algebra can be interpreted in the framework of curved momentum space leading to the relativity of locality [1]. We study the geometric properties of the momentum space described by κ-Poincaré, and derive the consequences for particles propagation and energy-momentum conservation laws in interaction vertices, obtaining for the first time a coherent and fully workable model of the deformed relativistic kinematics implied by κ-Poincaré. We describe the action of boost transformations on multi-particles systems, showing that in order to keep covariant the composed momenta it is necessary to introduce a dependence of the rapidity parameter on the particles momenta themselves. Finally, we show that this particular form of the boost transformations keeps the validity of the relativity principle, demonstrating the invariance of the equations of motion under boost transformations. arXiv:1106.5710v1 [gr-qc]

I introduce in κ-Minkowski noncommutative spacetime the basic tools of quantum differential geome... more I introduce in κ-Minkowski noncommutative spacetime the basic tools of quantum differential geometry, namely bicovariant differential calculus, Lie and inner derivatives, the integral, the Hodge- * and the metric. I show the relevance of these tools for field theory with an application to complex scalar field, for which I am able to identify a vector-valued four-form which generalizes the energy-momentum tensor. Its closedness is proved, expressing in a covariant form the conservation of energy-momentum.

Arxiv preprint arXiv:1106.0261, Jan 1, 2011

We question the emergence of a minimal length in quantum spacetime, confronting two notions that ... more We question the emergence of a minimal length in quantum spacetime, confronting two notions that appeared at various points in the literature: length as the spectrum of an operator L in the Doplicher Fredenhagen Roberts (DFR) quantum spacetime and the canonical noncommutative spacetime (θ-Minkowski) on the one side; Connes spectral distance in noncommutative geometry on the other side. Although on the Euclidean space -as well as on manifolds with suitable symmetry -the two notions merge into the one of geodesic distance, they yield distinct results in the noncommutative framework. In particular, the widespread idea that quantizing the coordinates inevitably yields a minimal length should be handle with care: on the Moyal plane for instance, both the quantum length d L (intended as the mean value of the length operator on a separable two-point state) and the spectral distance d D are discrete, but only the former is bounded above from zero. We propose a framework in which the comparison of d L with d D makes sense: by doubling the spectral triple, one turns the quantum length into a true distance function and, simultaneously, emphasises the "quantum mechanics flavor" of the spectral distance. Specifically, for any couple of identical states, d L is identified with the spectral distance on a two-sheet model (each state living on a distinct sheet). Using Pythagoras-like relations for spectral triples, we extend the identification to any couples of distinct states, provided the spectral distance d E on a single sheet coincides with a new distance d L induced by the length operator. This condition is not fulfilled on the Moyal plane. We interpret the discrepancy between d L and d E (which becomes negligible at high energy) as two distinct ways of integrating the line element on a quantum space. This leads us to propose an equation for a geodesic on the Moyal plane. * Pierre.Martinetti@roma1.infn.it † Flavio.Mercati@roma1.infn.it ‡ tomassini@sci.unich.it arXiv:1106.0261v1 [math-ph] 1 Jun 2011 * * Details on how a covariant Dirac operator modifies the metric can be found in e.g. [20] † † Notice that in the DFR model the quantum length between a state and itself constantly equals dL(ψ0, ψ0) (and is in fact minimum) if one considers only coherent states. Unfortunately dD between coherent states is still unknown, which forbids any comparison. This will be the subject of a future work.

Arxiv preprint arXiv:1106.5710, Jan 1, 2011

We show that the κ-Poincaré Hopf algebra can be interpreted in the framework of curved momentum s... more We show that the κ-Poincaré Hopf algebra can be interpreted in the framework of curved momentum space leading to the relativity of locality [1]. We study the geometric properties of the momentum space described by κ-Poincaré, and derive the consequences for particles propagation and energy-momentum conservation laws in interaction vertices, obtaining for the first time a coherent and fully workable model of the deformed relativistic kinematics implied by κ-Poincaré. We describe the action of boost transformations on multi-particles systems, showing that in order to keep covariant the composed momenta it is necessary to introduce a dependence of the rapidity parameter on the particles momenta themselves. Finally, we show that this particular form of the boost transformations keeps the validity of the relativity principle, demonstrating the invariance of the equations of motion under boost transformations. arXiv:1106.5710v1 [gr-qc]

… Field Theories: Pescara, Italy, 3-8 …, Jan 1, 2008

We consider some alternative scenarios for the fate of Poincaré/Lorentz symmetry at the Planck sc... more We consider some alternative scenarios for the fate of Poincaré/Lorentz symmetry at the Planck scale, and we discuss some opportunities to test these scenarios.

Arxiv preprint arXiv:1004.3352, Jan 1, 2010

We advocate a novel perspective on the phenomenology of a framework with spacetime noncommutativi... more We advocate a novel perspective on the phenomenology of a framework with spacetime noncommutativity which is of established relevance for string theory. Our analysis applies to cases in which the noncommutativity parameters are arranged according to the criteria of "light-like noncommutativity" and ultraviolet supersymmetry is assumed, so that the implications of the characteristic mechanism of ultraviolet/infrared mixing are relatively soft. We also observe that an analogous case of soft ultraviolet-infrared mixing is present in a previously-proposed Loop-quantum-gravity-inspired description of quantum spacetime. And we show that soft ultraviolet-infrared mixing produces an anomaly for the nonrelativistic de Broglie relation λv = h/m, with correction term governed by a single (but particle-dependent) parameter χ. We test this hypothesis by comparing a determination of the fine structure constant that relies on the de Broglie relation for nonrelativistic neutrons to other independent determinations of the fine structure constant, and we obtain an estimate of χ that differs from 0 with four-standard-deviation significance.

I briefly introduce the recently introduced idea of relativity of locality, which is a consequenc... more I briefly introduce the recently introduced idea of relativity of locality, which is a consequence of a non-flat geometry of momentum space. Momentum space can acquire nontrivial geometrical properties due to quantum gravity effects. I study the relation of this framework with noncommutative geometry, and the Quantum Group approach to noncommutative spaces. In particular I'm interested in kappa-Poincaré, which is a Quantum Group that, as shown by Freidel and Livine, in the 1+1D case emerges as the symmetry of effective field theory coupled with quantum gravity, once that the gravitational degrees of freedom are integrated out. I'm interested in particular in the Lorentz covariance of this model which is present, but is realized in a nontrivial way. If I still have time, I'll then speak about an under-course general study of the Lorentz covariance of Relative Locality models.

International Journal of …, Jan 1, 2010

The literature on quantum-gravity-inspired scenarios for the quantization of spacetime has so far... more The literature on quantum-gravity-inspired scenarios for the quantization of spacetime has so far focused on particle-physics-like studies. This is partly justified by the present limitations of our understanding of quantum-gravity theories, but we here argue that valuable insight can be gained through semi-heuristic analyses of the implications for gravitational phenomena of some results obtained in the quantumspacetime literature. In particular, we show that the types of description of particle propagation that emerged in certain quantum-spacetime frameworks have striking implications for gravitational collapse and for the behaviour of gravity at large distances.

Have our fundamental theories got time right? Does size really matter? Or is physics all in the e... more Have our fundamental theories got time right? Does size really matter? Or is physics all in the eyes of the beholder? In this essay, we question the origin of time and scale by reevaluating the nature of measurement. We then argue for a radical scenario, supported by a suggestive calculation, where the flow of time is inseparable from the measurement process. Our scenario breaks the bond of time and space and builds a new one: the marriage of time and scale.

Thesis not yet defended Flavio Mercati. A perspective on the theory and phenomenology of quantum ... more Thesis not yet defended Flavio Mercati. A perspective on the theory and phenomenology of quantum spacetime. Ph.D. thesis. Sapienza -University of Rome

Arxiv preprint arXiv:1105.1599, Jan 1, 2011

We present the star-product algebra of the κ-deformation of Minkowski space and the formulation o... more We present the star-product algebra of the κ-deformation of Minkowski space and the formulation of Poincaré covariant differential calculus. We use these tools to construct a twisted K-cycle over the algebra and a twisted cyclic cocycle.

Arxiv preprint arXiv: …, Jan 1, 2007

We summarize here the first results obtained using a technique we recently developed for the Noet... more We summarize here the first results obtained using a technique we recently developed for the Noether analysis of Hopf-algebra spacetime symmetries, including the derivation of conserved charges for field theories in noncommutative spacetimes of canonical or κ-Minkowski type. * Based in part on the lecture given by G.A.-C. at the 21st Nishinomiya-Yukawa Memorial Symposium Noncommutative geometry and quantum spacetime in physics, but updated on the basis of the related results more recently obtained in Refs.

AIP Conference Proceedings, Jan 1, 2010

We reexamine the motivation for ultraviolet∕ infrared mixing in quantum gravity and some of the q... more We reexamine the motivation for ultraviolet∕ infrared mixing in quantum gravity and some of the quantum‐spacetime formalizations where it has been found. We then focus on cases in which the infrared manifestations of the mixing are relatively soft, arguing that they can motivate a particularly appealing phenomenology. Among the possible implications for the large‐distance behavior of gravity one intriguingly finds a correction with logarithmic dependence on distance. And one can explain in terms of soft ultraviolet∕ infrared mixing ...