Relativistic Phase Space Arising out of the Dirac Algebra

1983 ◽  
pp. 67-76 ◽  
Author(s):  
D. Bohm ◽  
B. J. Hiley
Keyword(s):  
Phase Space ◽  
Dirac Algebra ◽  
Relativistic Phase

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.

scholarly journals Comment on ‘‘Nonlinear resonance and chaos in the relativistic phase space for driven nonlinear systems’’

1996 ◽  
Vol 53 (4) ◽  
pp. 4240-4241 ◽  
Author(s):  
D. G. Luchinsky ◽  
P. V. E. McClintock ◽  
S. M. Soskin ◽  
N. D. Stein ◽  
A. B. Neiman
Keyword(s):  
Phase Space ◽  
Nonlinear Systems ◽  
Nonlinear Resonance ◽  
Relativistic Phase

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 Relativistic phase space: dimensional recurrences

2003 ◽  
Vol 36 (6) ◽  
pp. 1719-1727 ◽  
Author(s):  
R Delbourgo ◽  
M L Roberts
Keyword(s):  
Phase Space ◽  
Relativistic Phase

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.

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