Daniele Pranzetti | SISSA - Academia.edu (original) (raw)

Papers by Daniele Pranzetti

By reintroducing Lorentz invariance in canonical loop quantum gravity, we define a geometrical no... more By reintroducing Lorentz invariance in canonical loop quantum gravity, we define a geometrical notion of temperature for quantum isolated horizons. This is done by demanding that the horizon state satisfying the boundary conditions be a Kubo-Martin-Schwinger state. The exact formula for the temperature can be derived by imposing the reality conditions in the form of the linear simplicity constraints for an imaginary Barbero-Immirzi parameter. Thus, our analysis reveals the connection between the analytic continuation to the Ashtekar self-dual variables and the thermality of the horizon. The horizon thermal equilibrium state can then be used to compute both the entanglement and the Boltzmann entropies. We show that the two provide the same finite answer, which allows us to recover the Bekenstein-Hawking formula in the semi-classical limit. In this way, we shed new light on the microscopic origin of black hole entropy by revealing the equivalence between the near-horizon degrees of freedom entanglement proposal and the state-counting interpretation. The connection with the Connes-Rovelli thermal time proposal for a general relativistic statistical mechanics is worked out.

Physical Review D

We model spherically symmetric black holes within the group field theory formalism for quantum gr... more We model spherically symmetric black holes within the group field theory formalism for quantum gravity via generalized condensate states, involving sums over arbitrarily refined graphs (dual to threedimensional triangulations). The construction relies heavily on both the combinatorial tools of random tensor models and the quantum geometric data of loop quantum gravity, both part of the group field theory formalism. Armed with the detailed microscopic structure, we compute the entropy associated with the black hole horizon, which turns out to be equivalently the Boltzmann entropy of its microscopic degrees of freedom and the entanglement entropy between the inside and outside regions. We recover the area law under very general conditions, as well as the Bekenstein-Hawking formula. The result is also shown to be generically independent of any specific value of the Immirzi parameter.

Using the recent thermodynamical study of isolated horizons by Ghosh and Perez, we provide a stat... more Using the recent thermodynamical study of isolated horizons by Ghosh and Perez, we provide a statistical mechanical analysis of isolated horizons near equilibrium in the grand canonical ensemble. By matching the description of the dynamical phase in terms of weakly dynamical horizons with this local statistical framework, we introduce a notion of temperature in terms of the local surface gravity. This provides further support to the recovering of the semiclassical area law just by means of thermodynamical considerations. Moreover, it allows us to study the radiation process generated by the LQG dynamics near the horizon, providing a quantum gravity description of the horizon evaporation. For large black holes, the spectrum we derive presents a discrete structure which could be potentially observable and might be preserved even after the inclusion of all the relevant transition lines.

Physical Review D, 2014

By reintroducing Lorentz invariance in canonical loop quantum gravity, we define a geometrical no... more By reintroducing Lorentz invariance in canonical loop quantum gravity, we define a geometrical notion of temperature for quantum isolated horizons. This is done by demanding that the horizon state satisfying the boundary conditions be a Kubo-Martin-Schwinger state. The exact formula for the temperature can be derived by imposing the reality conditions in the form of the linear simplicity constraints for an imaginary Barbero-Immirzi parameter. Thus, our analysis reveals the connection between the analytic continuation to the Ashtekar self-dual variables and the thermality of the horizon. The horizon thermal equilibrium state can then be used to compute both the entanglement and the Boltzmann entropies. We show that the two provide the same finite answer, which allows us to recover the Bekenstein-Hawking formula in the semi-classical limit. In this way, we shed new light on the microscopic origin of black hole entropy by revealing the equivalence between the near-horizon degrees of freedom entanglement proposal and the state-counting interpretation.

Physical Review Letters, 2012

Using the recent thermodynamical study of isolated horizons by Ghosh and Perez, we provide a stat... more Using the recent thermodynamical study of isolated horizons by Ghosh and Perez, we provide a statistical mechanical analysis of isolated horizons near equilibrium in the grand canonical ensemble. By matching the description of the dynamical phase in terms of weakly dynamical horizons with this local statistical framework, we introduce a notion of temperature in terms of the local surface gravity. This provides further support to the recovering of the semiclassical area law just by means of thermodynamical considerations. Moreover, it allows us to study the radiation process generated by the LQG dynamics near the horizon, providing a quantum gravity description of the horizon evaporation. For large black holes, the spectrum we derive presents a discrete structure which could be potentially observable and might be preserved even after the inclusion of all the relevant transition lines.

Physical Review D, 2014

The Turaev-Viro state sum model provides a covariant spin foam quantization of three-dimensional ... more The Turaev-Viro state sum model provides a covariant spin foam quantization of three-dimensional Riemannian gravity with a positive cosmological constant Λ. We complete the program to canonically quantize the theory in the BF formulation using the formalism of Loop Quantum Gravity. In particular, we show first how quantum group structures arise from the requirement of the constraint algebra to be anomaly free. This allows us to generalize the construction of the physical scalar product, from the Λ = 0 case, in presence of a positive Λ. We prove the equivalence between the covariant and canonical quantizations by recovering the spin foam amplitudes. * daniele.pranzetti@gravity.fau.de

Classical and Quantum Gravity, 2013

We describe the black hole evaporation process driven by the dynamical evolution of the quantum g... more We describe the black hole evaporation process driven by the dynamical evolution of the quantum gravitational degrees of freedom resident at the horizon, as identified by the loop quantum gravity kinematics. Using a parallel with the Brownian motion, we interpret the first law of quantum dynamical horizon in terms of a fluctuation-dissipation relation. In this way, the horizon evolution is described in terms of relaxation to an equilibrium state balanced by the excitation of Planck scale constituents of the horizon. This discrete quantum hair structure associated to the horizon geometry produces a deviation from thermality in the radiation spectrum. We investigate the final stage of the evaporation process and show how the dynamics leads to the formation of a massive remnant, which can eventually decay.

Classical and Quantum Gravity, 2011

In this paper, I investigate the possible quantization, in the context of LQG, of three dimension... more In this paper, I investigate the possible quantization, in the context of LQG, of three dimensional gravity in the case of positive cosmological constant Λ and try to make contact with alternative quantization approaches already existing in the literature. Due to the appearance of an anomaly in the constraints algebra, previously studied as a first step of the analysis, alternative techniques developed for the quantization of systems with constraints algebras not associated with a structure Lie group need to be adopted. Therefore, I introduce an ansatz for a physical state which gives some transition amplitudes in agreement with what one would expect from the Turaev-Viro model. Moreover, in order to check that this state implements the right dynamicss, I show that it annihilates the master constraint for the theory up to the first order in Λ.

Journal of High Energy Physics, Mar 14, 2011

We study the state-counting problem that arises in the SU(2) black hole entropy calculation in lo... more We study the state-counting problem that arises in the SU(2) black hole entropy calculation in loop quantum gravity. More precisely, we compute the leading term and the logarithmic correction of both the spherically symmetric and the distorted SU(2) black holes. Contrary to what has been done in previous works, we have to take into account "quantum corrections" in our framework in the sense that the level k of the Chern-Simons theory which describes the black hole is finite and not sent to infinity. Therefore, the new results presented here allow for the computation of the entropy in models where the quantum group corrections are important.

) for a description of translation transformations based on a 4D differential calculus turn out t... more ) for a description of translation transformations based on a 4D differential calculus turn out to be applicable without any modification, and they allow us to show that the basis usually adopted for the 5D calculus does not take into account certain aspects of the structure of time translations in kappa\kappakappa-Minkowski. We propose a change of basis for the 5D calculus which leads to a more intuitive description of time translations.

We use the mathematical framework of loop quantum gravity (LQG) to study the quantization of thre... more We use the mathematical framework of loop quantum gravity (LQG) to study the quantization of three dimensional (Riemannian) gravity with positive cosmological constant (Lambda>0). We show that the usual regularization techniques (successful in the Lambda=0 case and widely applied in four dimensional LQG) lead to a deformation of the classical constraint algebra (or anomaly) proportional to the local strength of the curvature squared. We argue that this is an unavoidable consequence of the non-local nature of generalized connections.

Ijmpa, 2009

We perform a Noether analysis for a description of translation transformations in 4D kappa-Minkow... more We perform a Noether analysis for a description of translation transformations in 4D kappa-Minkowski noncommutative space-time which is based on the structure of a 5D differential calculus. The techniques that had been previously developed for a description of translation transformations based on a 4D differential calculus turn out to be applicable without any modification, and they allow us to show that the basis usually adopted for the 5D calculus does not take into account certain aspects of the structure of time translations in kappa-Minkowski. We propose a change of basis for the 5D calculus which leads to a more intuitive description of time translations.

Physics Letters B, 2015

We show that the spherically symmetric isolated horizon can be described in terms of an SU(2) con... more We show that the spherically symmetric isolated horizon can be described in terms of an SU(2) connection and a su(2) valued one form, obeying certain constraints. The horizon symplectic structure is precisely the one of 3d gravity in a first order formulation. We quantize the horizon degrees of freedom in the framework of loop quantum gravity, with methods recently developed for 3d gravity with non-vanishing cosmological constant. Bulk excitations ending on the horizon act very similar to particles in 3d gravity. The Bekenstein-Hawking law is recovered in the limit of imaginary Barbero-Immirzi parameter. Alternative methods of quantization are also discussed.

General Relativity and Gravitation, 2014

We construct a SU connection formulation of Kerr isolated horizons. As in the non-rotating case, ... more We construct a SU connection formulation of Kerr isolated horizons. As in the non-rotating case, the model is based on a SU (2) Chern-Simons theory describing the degrees of freedom on the horizon. The presence of a non-vanishing angular momentum modifies the admissibility conditions for spin network states. Physical states of the system are in correspondence with open intertwiners with total spin matching the angular momentum of the spacetime. PACS numbers: * Unité Mixte de Recherche (UMR 6207) du CNRS et Aix-Marseille Université; laboratoire affiliéà la FRUMAM (FR 2291).

Nuclear Physics B, 2014

A quantum isolated horizon can be modeled by an SU (2) Chern-Simons theory on a punctured 2-spher... more A quantum isolated horizon can be modeled by an SU (2) Chern-Simons theory on a punctured 2-sphere. We show how a local 2-dimensional conformal symmetry arises at each puncture inducing an infinite set of new observables localised at the horizon which satisfy a Kac-Moody algebra. By means of the isolated horizon boundary conditions, we represent the gravitational fluxes degrees of freedom in terms of the zero modes of the Kac-Moody algebra defined on the boundary of a punctured disk. In this way, our construction encodes a precise notion of CFT/gravity correspondence. The higher modes in the algebra represent new nongeometric charges which can be represented in terms of free matter field degrees of freedom. When computing the CFT partition function of the system, these new states induce an extra degeneracy factor, representing the density of horizon states at a given energy level, which reproduces the Bekenstein's holographic bound for an imaginary Immirzi parameter. This allows us to recover the Bekenstein-Hawking entropy formula without the large quantum gravity corrections associated with the number of punctures. * amit.ghosh@saha.ac.in

Journal of High Energy Physics, 2011

We study the state-counting problem that arises in the SU (2) black hole entropy calculation in l... more We study the state-counting problem that arises in the SU (2) black hole entropy calculation in loop quantum gravity. More precisely, we compute the leading term and the logarithmic correction of both the spherically symmetric and the distorted SU (2) black holes. Contrary to what has been done in previous works, we have to take into account "quantum corrections" in our framework in the sense that the level k of the Chern-Simons theory which describes the black hole is finite and not sent to infinity. Therefore, the new results presented here allow for the computation of the entropy in models where the quantum group corrections are important. * Fédération Denis Poisson Orléans-Tours, CNRS/UMR 6083 † Unité Mixte de Recherche (UMR 6207) du CNRS et des Universités Aix-Marseille I, Aix-Marseille II, et du Sud Toulon-Var; laboratoire afiliéà la FRUMAM (FR 2291)

Journal of High Energy Physics, 2011

1 See [9] for a more recent and alternative investigation of the link between the canonical quant... more 1 See [9] for a more recent and alternative investigation of the link between the canonical quantization of the Wheeler-DeWitt equation and the symmetries of the Ponzano-Regge model.

Symmetry, Integrability and Geometry: Methods and Applications, 2012

We review the black hole entropy calculation in the framework of Loop Quantum Gravity based on th... more We review the black hole entropy calculation in the framework of Loop Quantum Gravity based on the quasi-local definition of a black hole encoded in the isolated horizon formalism. We show, by means of the covariant phase space formalism, the appearance in the conserved symplectic structure of a boundary term corresponding to a Chern-Simons theory on the horizon and present its quantization both in the U (1) gauge fixed version and in the fully SU (2) invariant one. We then describe the boundary degrees of freedom counting techniques developed for an infinite value of the Chern-Simons level case and, less rigorously, for the case of a finite value. This allows us to perform a comparison between the U (1) and SU (2) approaches and provide a state of the art analysis of their common features and different implications for the entropy calculations. In particular, we comment on different points of view regarding the nature of the horizon degrees of freedom and the role played by the Barbero-Immirzi parameter. We conclude by presenting some of the most recent results concerning possible observational tests for theory.

Progress of Theoretical Physics Supplement, 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.

By reintroducing Lorentz invariance in canonical loop quantum gravity, we define a geometrical no... more By reintroducing Lorentz invariance in canonical loop quantum gravity, we define a geometrical notion of temperature for quantum isolated horizons. This is done by demanding that the horizon state satisfying the boundary conditions be a Kubo-Martin-Schwinger state. The exact formula for the temperature can be derived by imposing the reality conditions in the form of the linear simplicity constraints for an imaginary Barbero-Immirzi parameter. Thus, our analysis reveals the connection between the analytic continuation to the Ashtekar self-dual variables and the thermality of the horizon. The horizon thermal equilibrium state can then be used to compute both the entanglement and the Boltzmann entropies. We show that the two provide the same finite answer, which allows us to recover the Bekenstein-Hawking formula in the semi-classical limit. In this way, we shed new light on the microscopic origin of black hole entropy by revealing the equivalence between the near-horizon degrees of freedom entanglement proposal and the state-counting interpretation. The connection with the Connes-Rovelli thermal time proposal for a general relativistic statistical mechanics is worked out.

Physical Review D

We model spherically symmetric black holes within the group field theory formalism for quantum gr... more We model spherically symmetric black holes within the group field theory formalism for quantum gravity via generalized condensate states, involving sums over arbitrarily refined graphs (dual to threedimensional triangulations). The construction relies heavily on both the combinatorial tools of random tensor models and the quantum geometric data of loop quantum gravity, both part of the group field theory formalism. Armed with the detailed microscopic structure, we compute the entropy associated with the black hole horizon, which turns out to be equivalently the Boltzmann entropy of its microscopic degrees of freedom and the entanglement entropy between the inside and outside regions. We recover the area law under very general conditions, as well as the Bekenstein-Hawking formula. The result is also shown to be generically independent of any specific value of the Immirzi parameter.

Using the recent thermodynamical study of isolated horizons by Ghosh and Perez, we provide a stat... more Using the recent thermodynamical study of isolated horizons by Ghosh and Perez, we provide a statistical mechanical analysis of isolated horizons near equilibrium in the grand canonical ensemble. By matching the description of the dynamical phase in terms of weakly dynamical horizons with this local statistical framework, we introduce a notion of temperature in terms of the local surface gravity. This provides further support to the recovering of the semiclassical area law just by means of thermodynamical considerations. Moreover, it allows us to study the radiation process generated by the LQG dynamics near the horizon, providing a quantum gravity description of the horizon evaporation. For large black holes, the spectrum we derive presents a discrete structure which could be potentially observable and might be preserved even after the inclusion of all the relevant transition lines.

Physical Review D, 2014

By reintroducing Lorentz invariance in canonical loop quantum gravity, we define a geometrical no... more By reintroducing Lorentz invariance in canonical loop quantum gravity, we define a geometrical notion of temperature for quantum isolated horizons. This is done by demanding that the horizon state satisfying the boundary conditions be a Kubo-Martin-Schwinger state. The exact formula for the temperature can be derived by imposing the reality conditions in the form of the linear simplicity constraints for an imaginary Barbero-Immirzi parameter. Thus, our analysis reveals the connection between the analytic continuation to the Ashtekar self-dual variables and the thermality of the horizon. The horizon thermal equilibrium state can then be used to compute both the entanglement and the Boltzmann entropies. We show that the two provide the same finite answer, which allows us to recover the Bekenstein-Hawking formula in the semi-classical limit. In this way, we shed new light on the microscopic origin of black hole entropy by revealing the equivalence between the near-horizon degrees of freedom entanglement proposal and the state-counting interpretation.

Physical Review Letters, 2012

Using the recent thermodynamical study of isolated horizons by Ghosh and Perez, we provide a stat... more Using the recent thermodynamical study of isolated horizons by Ghosh and Perez, we provide a statistical mechanical analysis of isolated horizons near equilibrium in the grand canonical ensemble. By matching the description of the dynamical phase in terms of weakly dynamical horizons with this local statistical framework, we introduce a notion of temperature in terms of the local surface gravity. This provides further support to the recovering of the semiclassical area law just by means of thermodynamical considerations. Moreover, it allows us to study the radiation process generated by the LQG dynamics near the horizon, providing a quantum gravity description of the horizon evaporation. For large black holes, the spectrum we derive presents a discrete structure which could be potentially observable and might be preserved even after the inclusion of all the relevant transition lines.

Physical Review D, 2014

The Turaev-Viro state sum model provides a covariant spin foam quantization of three-dimensional ... more The Turaev-Viro state sum model provides a covariant spin foam quantization of three-dimensional Riemannian gravity with a positive cosmological constant Λ. We complete the program to canonically quantize the theory in the BF formulation using the formalism of Loop Quantum Gravity. In particular, we show first how quantum group structures arise from the requirement of the constraint algebra to be anomaly free. This allows us to generalize the construction of the physical scalar product, from the Λ = 0 case, in presence of a positive Λ. We prove the equivalence between the covariant and canonical quantizations by recovering the spin foam amplitudes. * daniele.pranzetti@gravity.fau.de

Classical and Quantum Gravity, 2013

We describe the black hole evaporation process driven by the dynamical evolution of the quantum g... more We describe the black hole evaporation process driven by the dynamical evolution of the quantum gravitational degrees of freedom resident at the horizon, as identified by the loop quantum gravity kinematics. Using a parallel with the Brownian motion, we interpret the first law of quantum dynamical horizon in terms of a fluctuation-dissipation relation. In this way, the horizon evolution is described in terms of relaxation to an equilibrium state balanced by the excitation of Planck scale constituents of the horizon. This discrete quantum hair structure associated to the horizon geometry produces a deviation from thermality in the radiation spectrum. We investigate the final stage of the evaporation process and show how the dynamics leads to the formation of a massive remnant, which can eventually decay.

Classical and Quantum Gravity, 2011

In this paper, I investigate the possible quantization, in the context of LQG, of three dimension... more In this paper, I investigate the possible quantization, in the context of LQG, of three dimensional gravity in the case of positive cosmological constant Λ and try to make contact with alternative quantization approaches already existing in the literature. Due to the appearance of an anomaly in the constraints algebra, previously studied as a first step of the analysis, alternative techniques developed for the quantization of systems with constraints algebras not associated with a structure Lie group need to be adopted. Therefore, I introduce an ansatz for a physical state which gives some transition amplitudes in agreement with what one would expect from the Turaev-Viro model. Moreover, in order to check that this state implements the right dynamicss, I show that it annihilates the master constraint for the theory up to the first order in Λ.

Journal of High Energy Physics, Mar 14, 2011

We study the state-counting problem that arises in the SU(2) black hole entropy calculation in lo... more We study the state-counting problem that arises in the SU(2) black hole entropy calculation in loop quantum gravity. More precisely, we compute the leading term and the logarithmic correction of both the spherically symmetric and the distorted SU(2) black holes. Contrary to what has been done in previous works, we have to take into account "quantum corrections" in our framework in the sense that the level k of the Chern-Simons theory which describes the black hole is finite and not sent to infinity. Therefore, the new results presented here allow for the computation of the entropy in models where the quantum group corrections are important.

) for a description of translation transformations based on a 4D differential calculus turn out t... more ) for a description of translation transformations based on a 4D differential calculus turn out to be applicable without any modification, and they allow us to show that the basis usually adopted for the 5D calculus does not take into account certain aspects of the structure of time translations in kappa\kappakappa-Minkowski. We propose a change of basis for the 5D calculus which leads to a more intuitive description of time translations.

We use the mathematical framework of loop quantum gravity (LQG) to study the quantization of thre... more We use the mathematical framework of loop quantum gravity (LQG) to study the quantization of three dimensional (Riemannian) gravity with positive cosmological constant (Lambda>0). We show that the usual regularization techniques (successful in the Lambda=0 case and widely applied in four dimensional LQG) lead to a deformation of the classical constraint algebra (or anomaly) proportional to the local strength of the curvature squared. We argue that this is an unavoidable consequence of the non-local nature of generalized connections.

Ijmpa, 2009

We perform a Noether analysis for a description of translation transformations in 4D kappa-Minkow... more We perform a Noether analysis for a description of translation transformations in 4D kappa-Minkowski noncommutative space-time which is based on the structure of a 5D differential calculus. The techniques that had been previously developed for a description of translation transformations based on a 4D differential calculus turn out to be applicable without any modification, and they allow us to show that the basis usually adopted for the 5D calculus does not take into account certain aspects of the structure of time translations in kappa-Minkowski. We propose a change of basis for the 5D calculus which leads to a more intuitive description of time translations.

Physics Letters B, 2015

We show that the spherically symmetric isolated horizon can be described in terms of an SU(2) con... more We show that the spherically symmetric isolated horizon can be described in terms of an SU(2) connection and a su(2) valued one form, obeying certain constraints. The horizon symplectic structure is precisely the one of 3d gravity in a first order formulation. We quantize the horizon degrees of freedom in the framework of loop quantum gravity, with methods recently developed for 3d gravity with non-vanishing cosmological constant. Bulk excitations ending on the horizon act very similar to particles in 3d gravity. The Bekenstein-Hawking law is recovered in the limit of imaginary Barbero-Immirzi parameter. Alternative methods of quantization are also discussed.

General Relativity and Gravitation, 2014

We construct a SU connection formulation of Kerr isolated horizons. As in the non-rotating case, ... more We construct a SU connection formulation of Kerr isolated horizons. As in the non-rotating case, the model is based on a SU (2) Chern-Simons theory describing the degrees of freedom on the horizon. The presence of a non-vanishing angular momentum modifies the admissibility conditions for spin network states. Physical states of the system are in correspondence with open intertwiners with total spin matching the angular momentum of the spacetime. PACS numbers: * Unité Mixte de Recherche (UMR 6207) du CNRS et Aix-Marseille Université; laboratoire affiliéà la FRUMAM (FR 2291).

Nuclear Physics B, 2014

A quantum isolated horizon can be modeled by an SU (2) Chern-Simons theory on a punctured 2-spher... more A quantum isolated horizon can be modeled by an SU (2) Chern-Simons theory on a punctured 2-sphere. We show how a local 2-dimensional conformal symmetry arises at each puncture inducing an infinite set of new observables localised at the horizon which satisfy a Kac-Moody algebra. By means of the isolated horizon boundary conditions, we represent the gravitational fluxes degrees of freedom in terms of the zero modes of the Kac-Moody algebra defined on the boundary of a punctured disk. In this way, our construction encodes a precise notion of CFT/gravity correspondence. The higher modes in the algebra represent new nongeometric charges which can be represented in terms of free matter field degrees of freedom. When computing the CFT partition function of the system, these new states induce an extra degeneracy factor, representing the density of horizon states at a given energy level, which reproduces the Bekenstein's holographic bound for an imaginary Immirzi parameter. This allows us to recover the Bekenstein-Hawking entropy formula without the large quantum gravity corrections associated with the number of punctures. * amit.ghosh@saha.ac.in

Journal of High Energy Physics, 2011

We study the state-counting problem that arises in the SU (2) black hole entropy calculation in l... more We study the state-counting problem that arises in the SU (2) black hole entropy calculation in loop quantum gravity. More precisely, we compute the leading term and the logarithmic correction of both the spherically symmetric and the distorted SU (2) black holes. Contrary to what has been done in previous works, we have to take into account "quantum corrections" in our framework in the sense that the level k of the Chern-Simons theory which describes the black hole is finite and not sent to infinity. Therefore, the new results presented here allow for the computation of the entropy in models where the quantum group corrections are important. * Fédération Denis Poisson Orléans-Tours, CNRS/UMR 6083 † Unité Mixte de Recherche (UMR 6207) du CNRS et des Universités Aix-Marseille I, Aix-Marseille II, et du Sud Toulon-Var; laboratoire afiliéà la FRUMAM (FR 2291)

Journal of High Energy Physics, 2011

1 See [9] for a more recent and alternative investigation of the link between the canonical quant... more 1 See [9] for a more recent and alternative investigation of the link between the canonical quantization of the Wheeler-DeWitt equation and the symmetries of the Ponzano-Regge model.

Symmetry, Integrability and Geometry: Methods and Applications, 2012

We review the black hole entropy calculation in the framework of Loop Quantum Gravity based on th... more We review the black hole entropy calculation in the framework of Loop Quantum Gravity based on the quasi-local definition of a black hole encoded in the isolated horizon formalism. We show, by means of the covariant phase space formalism, the appearance in the conserved symplectic structure of a boundary term corresponding to a Chern-Simons theory on the horizon and present its quantization both in the U (1) gauge fixed version and in the fully SU (2) invariant one. We then describe the boundary degrees of freedom counting techniques developed for an infinite value of the Chern-Simons level case and, less rigorously, for the case of a finite value. This allows us to perform a comparison between the U (1) and SU (2) approaches and provide a state of the art analysis of their common features and different implications for the entropy calculations. In particular, we comment on different points of view regarding the nature of the horizon degrees of freedom and the role played by the Barbero-Immirzi parameter. We conclude by presenting some of the most recent results concerning possible observational tests for theory.

Progress of Theoretical Physics Supplement, 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.