scholarly journals GEOMETRIC STRUCTURES OF THE CLASSICAL GENERAL RELATIVISTIC PHASE SPACE

2008 ◽  
Vol 05 (05) ◽  
pp. 699-754 ◽  
Author(s):  
JOSEF JANYŠKA ◽  
MARCO MODUGNO
Keyword(s):  
Electromagnetic Field ◽  
Phase Space ◽  
Relativistic Particle ◽  
Jet Space ◽  
Geometric Structures ◽  
Geometric Properties ◽  
Geometric Conditions ◽  
General Relativistic ◽  
Relativistic Phase

This paper is concerned with basic geometric properties of the phase space of a classical general relativistic particle, regarded as the 1st jet space of motions, i.e. as the 1st jet space of timelike 1-dimensional submanifolds of spacetime. This setting allows us to skip constraints. Our main goal is to determine the geometric conditions by which the Lorentz metric and a connection of the phase space yield contact and Jacobi structures. In particular, we specialize these conditions to the cases when the connection of the phase space is generated by the metric and an additional tensor. Indeed, the case generated by the metric and the electromagnetic field is included, as well.

Remarks on infinitesimal symmetries of geometrical structures of the classical phase space of general relativistic test particle

2015 ◽  
Vol 12 (08) ◽  
pp. 1560020 ◽  
Author(s):  
Josef Janyška
Keyword(s):  
Electromagnetic Field ◽  
Phase Space ◽  
Test Particle ◽  
Contact Structure ◽  
Jet Space ◽  
Geometrical Structures ◽  
Lorentzian Metric ◽  
Dimensional Phase Space ◽  
General Relativistic ◽  
Classical Phase Space

The phase space of general relativistic test particle is defined as the 1-jet space of motions. A Lorentzian metric and an electromagnetic field define the joined almost-cosymplectic-contact structure on the odd-dimensional phase space. In this paper, we study infinitesimal symmetries (ISs) of this phase structure. We prove that there are no hidden ISs.

RELATIVISTIC PARTICLE WITH CURVATURE IN AN EXTERNAL ELECTROMAGNETIC FIELD

1991 ◽  
Vol 06 (22) ◽  
pp. 3989-3996 ◽  
Author(s):  
V.V. NESTERENKO
Keyword(s):  
Electromagnetic Field ◽  
Wave Equation ◽  
Phase Space ◽  
Dirac Equation ◽  
Relativistic Particle ◽  
Canonical Quantization ◽  
Hamiltonian Formalism ◽  
External Electromagnetic Field ◽  
Operator Form ◽  
Complete Set

A model of a relativistic particle with curvature interacting with an external electromagnetic field in a “minimal way” is investigated. The generalized Hamiltonian formalism for this model is constructed. A complete set of the constraints in the phase space is obtained and then divided into first- and second-class constraints. On this basis the canonical quantization of the model is considered. A wave equation in the operator form, resembling the Dirac equation in an external electromagnetic field, is obtained. The massless version of this model is briefly discussed.

scholarly journals PHASE-SPACE CONSTRAINTS ON NEUTRINO LUMINOSITIES

2008 ◽  
Vol 23 (17n20) ◽  
pp. 1470-1477 ◽  
Author(s):  
C. SIVARAM ◽  
KENATH ARUN ◽  
C. A. SAMARTHA
Keyword(s):  
Phase Space ◽  
Neutrino Emission ◽  
Gravitational Clustering ◽  
General Relativistic ◽  
Compact Sources ◽  
Relativistic Phase

While the importance of phase space constraints for gravitational clustering of neutrinos (which are fermions) is well recognized, the explicit use of such constraints to limit neutrino emission from ultra energetic sources has not been stressed. Special and general relativistic phase space constraints are shown to limit neutrino luminosities in compact sources in various situations.

scholarly journals An Introduction to κ-Deformed Symmetries, Phase Spaces and Field Theory

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 946
Author(s):  
Michele Arzano ◽  
Jerzy Kowalski-Glikman
Keyword(s):  
Field Theory ◽  
Phase Space ◽  
Scalar Field ◽  
Lie Groups ◽  
Relativistic Particle ◽  
Deformed Symmetries ◽  
Poincaré Algebra ◽  
Free Scalar ◽  
Poisson Lie Groups ◽  
Relativistic Phase

In this review, we give a basic introduction to the κ-deformed relativistic phase space and free quantum fields. After a review of the κ-Poincaré algebra, we illustrate the construction of the κ-deformed phase space of a classical relativistic particle using the tools of Lie bi-algebras and Poisson–Lie groups. We then discuss how to construct a free scalar field theory on the non-commutative κ-Minkowski space associated to the κ-Poincaré and illustrate how the group valued nature of momenta affects the field propagation.

Special bracket versus Jacobi bracket on the classical phase space of general relativistic test particle

2014 ◽  
Vol 11 (07) ◽  
pp. 1460020 ◽  
Author(s):  
Josef Janyška
Keyword(s):  
Phase Space ◽  
Test Particle ◽  
Jet Space ◽  
Hamiltonian Approach ◽  
One Dimensional ◽  
Lie Bracket ◽  
General Relativistic ◽  
Jacobi Bracket ◽  
Classical Phase Space ◽  
Phase Functions

The classical phase space of general relativistic classical test particle (here called, for short, "phase space") is defined as the first jet space of motions regarded as timelike one-dimensional submanifolds of spacetime. By the projectability assumption, we define the subsheaf of special phase functions with a special Lie bracket and we compare the Lie algebra of special phase functions with the structures obtained on the phase space by the standard Hamiltonian approach.

Remarks on the linking theory of shape dynamics

2018 ◽  
Vol 15 (06) ◽  
pp. 1850098
Author(s):  
P. P. Yu
Keyword(s):  
Phase Space ◽  
Vector Bundle ◽  
Short Note ◽  
Extended Phase Space ◽  
Geometric Structures ◽  
Extended Phase ◽  
Shape Dynamics ◽  
Canonical Gravity ◽  
Alternative Description ◽  
Gauge Fixing

This short note is an attempt to bring out the geometric structures in the linking theory of shape dynamics. Symplectic induction is applied to give a natural construction of the extended phase space used in the linking theory as a trivial vector bundle over the original phase space for canonical gravity. The geometry of the gauge fixing for shape dynamics is analyzed with the assistance of the Lichnerowicz–York equation lifted to the extended phase space. An alternative description is provided to show how the same geometry simply derives from symplectic induction.

scholarly journals Charged radiating stars with Lie symmetries

2019 ◽  
Vol 79 (10) ◽  
Author(s):  
G. Z. Abebe ◽  
S. D. Maharaj
Keyword(s):  
Electromagnetic Field ◽  
Differential Equations ◽  
Equations Of State ◽  
Lie Symmetries ◽  
Boundary Equation ◽  
Symmetries Of Differential Equations ◽  
Radiating Stars ◽  
Barotropic Equation ◽  
Radiating Star ◽  
General Relativistic

Abstract We consider the general model of an accelerating, expanding and shearing radiating star in the presence of charge. Using a new set of variables arising from the Lie symmetries of differential equations we transform the boundary equation into ordinary differential equations. We present several new exact models for a charged gravitating sphere. A particular family of solution may be interpreted as a generalised Euclidean star in the presence of the electromagnetic field. This family admits a linear barotropic equation of state. In the uncharged limit, we regain general relativistic stellar models where proper and areal radii are equal, and its generalisations. Our group theoretical approach selects the physically important cases of Euclidean stars and equations of state.

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