Guido Magnano | Università degli Studi di Torino (original) (raw)
Papers by Guido Magnano
The use of algebraic computing programs in studies of general relativity is discussed. Considerat... more The use of algebraic computing programs in studies of general relativity is discussed. Consideration is given to the SHEEP program for calculating the components of a tensor, the CLASSI program for classifying metrics using the Newman-Penrose formalism, and STENSOR for the manipulation of indicial tensor formulas. Examples of the applications of these programs are given, including the application of CLASSI
EPJ Web of Conferences, 2013
Extended theories of gravitation are naturally singled out by an analysis inspired by the Ehelers... more Extended theories of gravitation are naturally singled out by an analysis inspired by the Ehelers-Pirani-Schild framework. In this framework the structure of spacetime is described by a Weyl geometry which is enforced by dynamics. Standard General Relativity is just one possible theory within the class of extended theories of gravitation. Also all Palatini f (R) theories are shown to be extended theories of gravitation. This more general setting allows a more general interpretation scheme and more general possible couplings between gravity and matter. The definitions and constructions of extended theories will be reviewed. A general interpretation scheme will be considered for extended theories and some examples will be considered. EPJ Web of Conferences work without GR corrections and that it would be better to conceive a completely relativistic GPS which does not rest on Newtonian (wrong) assumptions.
EPJ Web of Conferences, 2013
Extended theories of gravitation are naturally singled out by an analysis inspired by the Ehelers... more Extended theories of gravitation are naturally singled out by an analysis inspired by the Ehelers-Pirani-Schild framework. In this framework the structure of spacetime is described by a Weyl geometry which is enforced by dynamics. Standard General Relativity is just one possible theory within the class of extended theories of gravitation. Also all Palatini f (R) theories are shown to be extended theories of gravitation. This more general setting allows a more general interpretation scheme and more general possible couplings between gravity and matter. The definitions and constructions of extended theories will be reviewed. A general interpretation scheme will be considered for extended theories and some examples will be considered. EPJ Web of Conferences work without GR corrections and that it would be better to conceive a completely relativistic GPS which does not rest on Newtonian (wrong) assumptions.
Reviews in Mathematical Physics, 2002
We show that for a class of dynamical systems, Hamiltonian with respect to three distinct Poisson... more We show that for a class of dynamical systems, Hamiltonian with respect to three distinct Poisson brackets (P 0 , P 1 , P 2 ), separation coordinates are provided by the common roots of a set of bivariate polynomials. These polynomials, which generalise those considered by E. Sklyanin in his algebro-geometric approach, are obtained from the knowledge of: (i) a common Casimir function for the two Poisson pencils (P 1 − λP 0 ) and (P 2 − µP 0 ); (ii) a suitable set of vector fields, preserving P 0 but transversal to its symplectic leaves. The frameworks is applied to Lax equations with spectral parameter, for which not only it establishes a theoretical link between the separation techniques of Sklyanin and of Magri, but also provides a more efficient "inverse" procedure to obtain separation variables, not involving the extraction of roots.
Psychometrika, 2013
The theoretical probability of misclassification in a mastery test is exactly computed using the ... more The theoretical probability of misclassification in a mastery test is exactly computed using the raw score probability distribution (in the Rasch model) as a function of the examinee's latent ability. The resulting misclassification probability curve, together with the latent ability distribution in the group of examinees, completely determines the expected rate of classification errors. It is shown that several distinct ability thresholds, playing different roles in connection to classification reliability, can be associated to a test with a single cut score. In particular, it is possible to define (and compute) two relevant ability intervals, which encapsulate the functioning of a mastery test (about and far from the cut score, respectively); the dependence of these intervals on the item difficulty spectrum is investigated. Extension to the 2PL model is also discussed, with emphasis on the effects of weighted scoring.
Physical Review D, 1994
We argue that in a nonlinear gravity theory (the Lagrangian being an arbitrary function of the cu... more We argue that in a nonlinear gravity theory (the Lagrangian being an arbitrary function of the curvature scalar R), which according to well-known results is dynamically equivalent to a self-gravitating scalar field in General Relativity, the true physical variables are exactly those which describe the equivalent general-relativistic model (these variables are known as Einstein frame). Whenever such variables cannot be defined, there are strong indications that the original theory is unphysical, in the sense that Minkowski space is unstable due to existence of negative-energy solutions close to it. To this aim we first clarify the global net of relationships between the nonlinear gravity theories, scalar-tensor theories and General Relativity, showing that in a sense these are "canonically conjugated" to each other. We stress that the isomorphisms are in most cases local; in the regions where these are defined, we explicitly show how to map, in the presence of matter, the Jordan frame to the Einstein one and backwards. We study energetics for asymptotically flat solutions for those Lagrangians which admit conformal rescaling to Einstein frame in the vicinity of flat space. This is based on the second-order dynamics obtained, without changing the metric, by the use of a Helmholtz Lagrangian. We prove for a large class of these Lagrangians that the ADM energy is positive for solutions close to flat space, and this is determined by the lowest-order terms, R + aR 2 , in the Lagrangian. The proof of this Positive Energy Theorem relies on the existence of the Einstein frame, since in the (Helmholtz-)Jordan frame the Dominant Energy Condition does not hold and the field variables are unrelated to the total energy of the system. This is why we regard the Jordan frame as unphysical, while the Einstein frame is physical and reveals the physical contents of the theory. The latter should hence be viewed as physically equivalent to a self-interacting general-relativistic scalar field.
Journal of Mathematical Physics, 1990
Journal of Geometry and Physics, 2007
A new Poisson structure on a subspace of the Kupershmidt algebra is defined. This Poisson structu... more A new Poisson structure on a subspace of the Kupershmidt algebra is defined. This Poisson structure, together with other two already known, allows to construct a trihamiltonian recurrence for an extension of the periodic Toda lattice with n particles. Some explicit examples of the construction and of the first integrals found in this way are given.
International Journal of Geometric Methods in Modern Physics, 2014
Classical and Quantum Gravity, 1988
... Marco Ferrarist, Mauro Francaviglial and Guido MagnanoP t Dipartimento di Matematica, Univers... more ... Marco Ferrarist, Mauro Francaviglial and Guido MagnanoP t Dipartimento di Matematica, Universita di Cagliari, via Ospedale 72,09100 Cagliari, Italy $: lstituto di Fisica ... In a very recent paper [9], Cecotti has shown how to generalise Whitt's result to the case of supergravity. ...
Classical and Quantum Gravity, 2002
We derive a generic identity which holds for the metric (i.e. variational) energymomentum tensor ... more We derive a generic identity which holds for the metric (i.e. variational) energymomentum tensor under any field transformation in any generally covariant classical Lagrangian field theory. The identity determines the conditions under which a symmetry of the Lagrangian is also a symmetry of the energy-momentum tensor. It turns out that the stress tensor acquires the symmetry if the Lagrangian has the symmetry in a generic curved spacetime. In this sense a field theory in flat spacetime is not self-contained. When the identity is applied to the gauge invariant spin-two field in Minkowski space, we obtain an alternative and direct derivation of a known no-go theorem: a linear gauge invariant spin-2 field, which is dynamically equivalent to linearized General Relativity, cannot have a gauge invariant metric energy-momentum tensor. This implies that attempts to define the notion of gravitational energy density in terms of the metric energy-momentum tensor in a field-theoretical formulation of gravity must fail.
Classical and Quantum Gravity, 1990
... We are grateful to Sergio Cecotti, Pietro FrC, Salvatore Mignemi and Andrea Pasquinucci for u... more ... We are grateful to Sergio Cecotti, Pietro FrC, Salvatore Mignemi and Andrea Pasquinucci for useful discussions, and to Lars Hornfeldt and Michael Bradley for having introduced us to the package STENSOR. ... Rev. D 37 858 Amendola L, Litterio M and Occhionero F 1989 Phys. ...
The second-order 'Legendre-transformed version' of a general quadratic theory which is ... more The second-order 'Legendre-transformed version' of a general quadratic theory which is not equivalent to general relativity is described in detail. What happens to the various fields appearing in it when coefficients are chosen to reproduce the so-called 'Lanczos Lagrangian' is examined. Many authors have conjectured that ghost excitations should decouple from the theory with this particular choice. The present analysis displays a behavior which could correspond to this phenomenon.
Annals of Physics, 2003
We present a systematic exposition of the Lagrangian field theory for the massive spin-two field ... more We present a systematic exposition of the Lagrangian field theory for the massive spin-two field generated in higher-derivative gravity upon reduction to a second-order theory by means of the appropriate Legendre transformation. It has been noticed by various authors that this nonlinear field overcomes the well known inconsistency of the theory for a linear massive spin-two field interacting with Einstein's gravity. Starting from a Lagrangian quadratically depending on the Ricci tensor of the metric, we explore the two possible second-order pictures usually called "(Helmholtz-)Jordan frame" and "Einstein frame". In spite of their mathematical equivalence, the two frames have different structural properties: in Einstein frame, the spin-two field is minimally coupled to gravity, while in the other frame it is necessarily coupled to the curvature, without a separate kinetic term. We prove that the theory admits a unique and linearly stable ground state solution, and that the equations of motion are consistent, showing that these results can be obtained independently in either frame (each frame therefore provides a self-contained theory). The full equations of motion and the (variational) energy-momentum tensor for the spin-two field in Einstein frame are given, and a simple but nontrivial exact solution to these equations is found. The comparison of the energy-momentum tensors for the spin-two field in the two frames suggests that the Einstein frame is physically more acceptable. We point out that the energy-momentum tensor generated by the Lagrangian of the linearized theory is unrelated to the corresponding tensor of the full theory. It is then argued that the ghost-like nature of the nonlinear spin-two field, found long ago in the linear approximation, may not be so harmful to classical stability issues, as has been expected.
The use of algebraic computing programs in studies of general relativity is discussed. Considerat... more The use of algebraic computing programs in studies of general relativity is discussed. Consideration is given to the SHEEP program for calculating the components of a tensor, the CLASSI program for classifying metrics using the Newman-Penrose formalism, and STENSOR for the manipulation of indicial tensor formulas. Examples of the applications of these programs are given, including the application of CLASSI
EPJ Web of Conferences, 2013
Extended theories of gravitation are naturally singled out by an analysis inspired by the Ehelers... more Extended theories of gravitation are naturally singled out by an analysis inspired by the Ehelers-Pirani-Schild framework. In this framework the structure of spacetime is described by a Weyl geometry which is enforced by dynamics. Standard General Relativity is just one possible theory within the class of extended theories of gravitation. Also all Palatini f (R) theories are shown to be extended theories of gravitation. This more general setting allows a more general interpretation scheme and more general possible couplings between gravity and matter. The definitions and constructions of extended theories will be reviewed. A general interpretation scheme will be considered for extended theories and some examples will be considered. EPJ Web of Conferences work without GR corrections and that it would be better to conceive a completely relativistic GPS which does not rest on Newtonian (wrong) assumptions.
EPJ Web of Conferences, 2013
Extended theories of gravitation are naturally singled out by an analysis inspired by the Ehelers... more Extended theories of gravitation are naturally singled out by an analysis inspired by the Ehelers-Pirani-Schild framework. In this framework the structure of spacetime is described by a Weyl geometry which is enforced by dynamics. Standard General Relativity is just one possible theory within the class of extended theories of gravitation. Also all Palatini f (R) theories are shown to be extended theories of gravitation. This more general setting allows a more general interpretation scheme and more general possible couplings between gravity and matter. The definitions and constructions of extended theories will be reviewed. A general interpretation scheme will be considered for extended theories and some examples will be considered. EPJ Web of Conferences work without GR corrections and that it would be better to conceive a completely relativistic GPS which does not rest on Newtonian (wrong) assumptions.
Reviews in Mathematical Physics, 2002
We show that for a class of dynamical systems, Hamiltonian with respect to three distinct Poisson... more We show that for a class of dynamical systems, Hamiltonian with respect to three distinct Poisson brackets (P 0 , P 1 , P 2 ), separation coordinates are provided by the common roots of a set of bivariate polynomials. These polynomials, which generalise those considered by E. Sklyanin in his algebro-geometric approach, are obtained from the knowledge of: (i) a common Casimir function for the two Poisson pencils (P 1 − λP 0 ) and (P 2 − µP 0 ); (ii) a suitable set of vector fields, preserving P 0 but transversal to its symplectic leaves. The frameworks is applied to Lax equations with spectral parameter, for which not only it establishes a theoretical link between the separation techniques of Sklyanin and of Magri, but also provides a more efficient "inverse" procedure to obtain separation variables, not involving the extraction of roots.
Psychometrika, 2013
The theoretical probability of misclassification in a mastery test is exactly computed using the ... more The theoretical probability of misclassification in a mastery test is exactly computed using the raw score probability distribution (in the Rasch model) as a function of the examinee's latent ability. The resulting misclassification probability curve, together with the latent ability distribution in the group of examinees, completely determines the expected rate of classification errors. It is shown that several distinct ability thresholds, playing different roles in connection to classification reliability, can be associated to a test with a single cut score. In particular, it is possible to define (and compute) two relevant ability intervals, which encapsulate the functioning of a mastery test (about and far from the cut score, respectively); the dependence of these intervals on the item difficulty spectrum is investigated. Extension to the 2PL model is also discussed, with emphasis on the effects of weighted scoring.
Physical Review D, 1994
We argue that in a nonlinear gravity theory (the Lagrangian being an arbitrary function of the cu... more We argue that in a nonlinear gravity theory (the Lagrangian being an arbitrary function of the curvature scalar R), which according to well-known results is dynamically equivalent to a self-gravitating scalar field in General Relativity, the true physical variables are exactly those which describe the equivalent general-relativistic model (these variables are known as Einstein frame). Whenever such variables cannot be defined, there are strong indications that the original theory is unphysical, in the sense that Minkowski space is unstable due to existence of negative-energy solutions close to it. To this aim we first clarify the global net of relationships between the nonlinear gravity theories, scalar-tensor theories and General Relativity, showing that in a sense these are "canonically conjugated" to each other. We stress that the isomorphisms are in most cases local; in the regions where these are defined, we explicitly show how to map, in the presence of matter, the Jordan frame to the Einstein one and backwards. We study energetics for asymptotically flat solutions for those Lagrangians which admit conformal rescaling to Einstein frame in the vicinity of flat space. This is based on the second-order dynamics obtained, without changing the metric, by the use of a Helmholtz Lagrangian. We prove for a large class of these Lagrangians that the ADM energy is positive for solutions close to flat space, and this is determined by the lowest-order terms, R + aR 2 , in the Lagrangian. The proof of this Positive Energy Theorem relies on the existence of the Einstein frame, since in the (Helmholtz-)Jordan frame the Dominant Energy Condition does not hold and the field variables are unrelated to the total energy of the system. This is why we regard the Jordan frame as unphysical, while the Einstein frame is physical and reveals the physical contents of the theory. The latter should hence be viewed as physically equivalent to a self-interacting general-relativistic scalar field.
Journal of Mathematical Physics, 1990
Journal of Geometry and Physics, 2007
A new Poisson structure on a subspace of the Kupershmidt algebra is defined. This Poisson structu... more A new Poisson structure on a subspace of the Kupershmidt algebra is defined. This Poisson structure, together with other two already known, allows to construct a trihamiltonian recurrence for an extension of the periodic Toda lattice with n particles. Some explicit examples of the construction and of the first integrals found in this way are given.
International Journal of Geometric Methods in Modern Physics, 2014
Classical and Quantum Gravity, 1988
... Marco Ferrarist, Mauro Francaviglial and Guido MagnanoP t Dipartimento di Matematica, Univers... more ... Marco Ferrarist, Mauro Francaviglial and Guido MagnanoP t Dipartimento di Matematica, Universita di Cagliari, via Ospedale 72,09100 Cagliari, Italy $: lstituto di Fisica ... In a very recent paper [9], Cecotti has shown how to generalise Whitt's result to the case of supergravity. ...
Classical and Quantum Gravity, 2002
We derive a generic identity which holds for the metric (i.e. variational) energymomentum tensor ... more We derive a generic identity which holds for the metric (i.e. variational) energymomentum tensor under any field transformation in any generally covariant classical Lagrangian field theory. The identity determines the conditions under which a symmetry of the Lagrangian is also a symmetry of the energy-momentum tensor. It turns out that the stress tensor acquires the symmetry if the Lagrangian has the symmetry in a generic curved spacetime. In this sense a field theory in flat spacetime is not self-contained. When the identity is applied to the gauge invariant spin-two field in Minkowski space, we obtain an alternative and direct derivation of a known no-go theorem: a linear gauge invariant spin-2 field, which is dynamically equivalent to linearized General Relativity, cannot have a gauge invariant metric energy-momentum tensor. This implies that attempts to define the notion of gravitational energy density in terms of the metric energy-momentum tensor in a field-theoretical formulation of gravity must fail.
Classical and Quantum Gravity, 1990
... We are grateful to Sergio Cecotti, Pietro FrC, Salvatore Mignemi and Andrea Pasquinucci for u... more ... We are grateful to Sergio Cecotti, Pietro FrC, Salvatore Mignemi and Andrea Pasquinucci for useful discussions, and to Lars Hornfeldt and Michael Bradley for having introduced us to the package STENSOR. ... Rev. D 37 858 Amendola L, Litterio M and Occhionero F 1989 Phys. ...
The second-order 'Legendre-transformed version' of a general quadratic theory which is ... more The second-order 'Legendre-transformed version' of a general quadratic theory which is not equivalent to general relativity is described in detail. What happens to the various fields appearing in it when coefficients are chosen to reproduce the so-called 'Lanczos Lagrangian' is examined. Many authors have conjectured that ghost excitations should decouple from the theory with this particular choice. The present analysis displays a behavior which could correspond to this phenomenon.
Annals of Physics, 2003
We present a systematic exposition of the Lagrangian field theory for the massive spin-two field ... more We present a systematic exposition of the Lagrangian field theory for the massive spin-two field generated in higher-derivative gravity upon reduction to a second-order theory by means of the appropriate Legendre transformation. It has been noticed by various authors that this nonlinear field overcomes the well known inconsistency of the theory for a linear massive spin-two field interacting with Einstein's gravity. Starting from a Lagrangian quadratically depending on the Ricci tensor of the metric, we explore the two possible second-order pictures usually called "(Helmholtz-)Jordan frame" and "Einstein frame". In spite of their mathematical equivalence, the two frames have different structural properties: in Einstein frame, the spin-two field is minimally coupled to gravity, while in the other frame it is necessarily coupled to the curvature, without a separate kinetic term. We prove that the theory admits a unique and linearly stable ground state solution, and that the equations of motion are consistent, showing that these results can be obtained independently in either frame (each frame therefore provides a self-contained theory). The full equations of motion and the (variational) energy-momentum tensor for the spin-two field in Einstein frame are given, and a simple but nontrivial exact solution to these equations is found. The comparison of the energy-momentum tensors for the spin-two field in the two frames suggests that the Einstein frame is physically more acceptable. We point out that the energy-momentum tensor generated by the Lagrangian of the linearized theory is unrelated to the corresponding tensor of the full theory. It is then argued that the ghost-like nature of the nonlinear spin-two field, found long ago in the linear approximation, may not be so harmful to classical stability issues, as has been expected.