G. Vilasi
Università degli Studi di Salerno, Fisica E. R. Caianiello, Faculty Member
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This book contains papers presented at a conference on general relativity and gravitational physics. Topics covered include non-perturbative quantum gravity: a status report and stochastic quantization in curved space time.
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We describe a reduction procedure for dynamical systems. If Γ is a dynamical vector field on a manifold M, a reduced system is obtained by projecting Γ to a manifold Σ/≈ where Σ is a submanifold of M invariant under Γ and ≈ is a suitable... more
We describe a reduction procedure for dynamical systems. If Γ is a dynamical vector field on a manifold M, a reduced system is obtained by projecting Γ to a manifold Σ/≈ where Σ is a submanifold of M invariant under Γ and ≈ is a suitable equivalence relation.
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The Lie Group of projective transformations for dierent physical systems is considered. It is shown that many mathematically and physically relevant equations are projectively invariant. Classical and quantum systems of particles and... more
The Lie Group of projective transformations for dierent physical systems is considered. It is shown that many mathematically and physically relevant equations are projectively invariant. Classical and quantum systems of particles and their generalizations to kinetic theory and hydro-dynamics are considered from this new view point. New invariant equations and corresponding Conservation laws are introduced. The specic role of these transformations and The potential U (x) = jxj 2 with x 2 R n are discussed from physical and geometrical points of view. It is shown that all the considered examples are connected with a system of free particles. PACS:O3.20.+i,03.40.Gc,03.65 Fd 1
In the post-Galilean approximation, the Lagrangians are singular on a submanifold of the phase space. A general analysis of these peculiarities, which differ by the ones considered by Dirac, is, up to day, lacking. The analysis of the... more
In the post-Galilean approximation, the Lagrangians are singular on a submanifold of the phase space. A general analysis of these peculiarities, which differ by the ones considered by Dirac, is, up to day, lacking. The analysis of the dynamics of the one-dimensional and two-dimensional relativistic oscillators of the second tensor rank, is reported. A comparison with the cases of scalar and vector relativistic oscillators, described by a regular Lagrangian, is accomplished. Some equilibrium statistical properties of the relativistic oscillators are also analysed. 1. Introduction The approximation in which the corrections of order O(c \Gamma2 ), c denoting the light velocity, to the Galilei Group are taken in account, is called the post-Galilean approximation. The Postgalilean approximation has a quasi classical character. It seems to be sufficient for all known laboratory relativistic systems (e.g. high- temperature plasma in the investigations on the nuclear fusion where v 2 c ...
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An interesting connection between the Regge theory of scattering, the Veneziano amplitude, the Lee-Yang theorems in statistical mechanics and nonextensive Renyi entropy is addressed. In this scheme the standard entropy and the Renyi... more
An interesting connection between the Regge theory of scattering, the Veneziano amplitude, the Lee-Yang theorems in statistical mechanics and nonextensive Renyi entropy is addressed. In this scheme the standard entropy and the Renyi entropy appear to be different limits of a unique mathematical object. This framework sheds light on the physical origin of nonextensivity. A non trivial application to spin glass theory is shortly outlined.
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It is likely that the holographic principle will be a consequence of the would be theory of quantum gravity. Thus, it is interesting to try to go in the opposite direction: can the holographic principle fix the gravitational interaction?... more
It is likely that the holographic principle will be a consequence of the would be theory of quantum gravity. Thus, it is interesting to try to go in the opposite direction: can the holographic principle fix the gravitational interaction? It is shown that the classical gravitational interaction is well inside the set of potentials allowed by the holographic principle. Computations clarify which role such a principle could have in lowering the value of the cosmological constant computed in QFT to the observed one.
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Exact solutions of Einstein equations invariant for a 2-dimensional Lie algebra of Killing fields [X, Y] = Y, with Y of light type, are analyzed. The conditions for them to represent gravitational waves are established and the definition... more
Exact solutions of Einstein equations invariant for a 2-dimensional Lie algebra of Killing fields [X, Y] = Y, with Y of light type, are analyzed. The conditions for them to represent gravitational waves are established and the definition of energy and polarization is addressed. PACS numbers: 04.20.-q, 04.20.Gz, 04.20.Jb
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Exact solutions of Einstein field equations invariant for a non-Abelian 2-dimensional Lie algebra of Killing fields are described. Physical properties of these gravitational fields are studied, their wave character is checked by making... more
Exact solutions of Einstein field equations invariant for a non-Abelian 2-dimensional Lie algebra of Killing fields are described. Physical properties of these gravitational fields are studied, their wave character is checked by making use of covariant criteria and the observable effects of such waves are outlined. The possibility of detection of these waves with modern detectors, spherical resonant antennas in particular, is sketched.
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Non-vacuum exact gravitational waves invariant for a non Abelian two-dimensional Lie algebra generated by two Killing fields whose commutator is of light type, are described. The polarization of these waves, already known from previous... more
Non-vacuum exact gravitational waves invariant for a non Abelian two-dimensional Lie algebra generated by two Killing fields whose commutator is of light type, are described. The polarization of these waves, already known from previous works, is related to the sources. Non vacuum exact gravitational waves admitting only one Killing field of light type are also discussed. Because of experimental efforts devoted to the detection of gravitational waves, there is a growing theoretical interest in describing the emission of detectable gravitational waves from astrophysical sources. All experimental devices , laser interferometers or resonant antennas, need very precise theoretical predictions, and usually they are calibrated according to results of linearized theory. In fact, it is commonly believed that, since the sources are very far from the earth, the wave's amplitude is so small at the earth surface that the use of the linearized theory is lawful. However, in some cases this ass...
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Gravitational fields invariant for a non Abelian Lie algebra generating a 2-dimensional distribution, are explicitly described. When the orthogonal distribution is integrable and the metric is not degenerate along the orbits, these... more
Gravitational fields invariant for a non Abelian Lie algebra generating a 2-dimensional distribution, are explicitly described. When the orthogonal distribution is integrable and the metric is not degenerate along the orbits, these solutions are parameterized either by solutions of a transcendental equation (the tortoise equation), or by solutions of Darboux equation. Metrics, corresponding to solutions of the tortoise equation, are
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... _4t~al. Appl.. 5, 18 (1971). (a) F. MaGRI: Leet. Notes in Phys., 120, 233 (1980). (4) P . J . 0LVl~R: .7. 3Ialh. Phys. ... Our notation is a direct transcription of the usual one to the infinite-dimensional ease. Page 3. PHASE... more
... _4t~al. Appl.. 5, 18 (1971). (a) F. MaGRI: Leet. Notes in Phys., 120, 233 (1980). (4) P . J . 0LVl~R: .7. 3Ialh. Phys. ... Our notation is a direct transcription of the usual one to the infinite-dimensional ease. Page 3. PHASE MANIFOLD GEO~IETRY OF BURGERS IlIERARCIIY ...
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... whole re-gions of analyticity. In Sect. 3.7, we apply the contour integration method and derive the completeness relation for the Jost solutions of L(λ). This relation can be viewed as the spectral decomposition of L(λ). In this, and... more
... whole re-gions of analyticity. In Sect. 3.7, we apply the contour integration method and derive the completeness relation for the Jost solutions of L(λ). This relation can be viewed as the spectral decomposition of L(λ). In this, and ...
ABSTRACT The light can be a source of nonlinear gravitational waves corresponding (from a quantum point of view) to spin-1 massless particles. This fact suggests a possible solution of the old problem raised by Tolman, Ehrenfest, Podolsky... more
ABSTRACT The light can be a source of nonlinear gravitational waves corresponding (from a quantum point of view) to spin-1 massless particles. This fact suggests a possible solution of the old problem raised by Tolman, Ehrenfest, Podolsky and Wheeler, concerning the lack of attraction of two light pencils moving parallel.
ABSTRACT We introduce the notion of a real Hamiltonian form (RHF) of a dynamical system in analogy with the notion of real forms for simple Lie algebras. We first complexify the initial dynamical system and then restrict it to a subspace... more
ABSTRACT We introduce the notion of a real Hamiltonian form (RHF) of a dynamical system in analogy with the notion of real forms for simple Lie algebras. We first complexify the initial dynamical system and then restrict it to a subspace isomorphic (but not symplectomorphic) to the initial phase space. Thus to each real Hamiltonian system we are able to associate a family of nonequivalent RHF's. A crucial role in this construction is played by a compatible involution leaving invariant the Hamiltonian mimicking the properties of complex conjugation. If the initial system is integrable, its RHF's will also be integrable. This provides a method of finding new integrable systems starting from known ones. We construct several RHF's for a family of Calogero-Moser Hamiltonians.