scholarly journals GUP-BASED AND SNYDER NONCOMMUTATIVE ALGEBRAS, RELATIVISTIC PARTICLE MODELS, DEFORMED SYMMETRIES AND INTERACTION: A UNIFIED APPROACH

2013 ◽  
Vol 28 (27) ◽  
pp. 1350131 ◽  
Author(s):  
SOUVIK PRAMANIK ◽  
SUBIR GHOSH
Keyword(s):  
Relativistic Particle ◽  
Generalized Uncertainty Principle ◽  
External Electromagnetic Field ◽  
Point Particle ◽  
Dynamical Analysis ◽  
Lagrangian Model ◽  
Nonlinear Constraints ◽  
Unified Approach ◽  
Deformed Symmetries ◽  
Noncommutative Algebras

We have developed a unified scheme for studying noncommutative algebras based on generalized uncertainty principle (GUP) and Snyder form in a relativistically covariant point particle Lagrangian (or symplectic) framework. Even though the GUP-based algebra and Snyder algebra are very distinct, the more involved latter algebra emerges from an approximation of the Lagrangian model of the former algebra. Deformed Poincaré generators for the systems that keep space–time symmetries of the relativistic particle models have been studied thoroughly. From a purely constrained dynamical analysis perspective the models studied here are very rich and provide insights on how to consistently construct approximate models from the exact ones when nonlinear constraints are present in the system. We also study dynamics of the GUP particle in presence of external electromagnetic field.

BRST STOCHASTIC QUANTIZATION

1991 ◽  
Vol 06 (28) ◽  
pp. 4985-5015 ◽  
Author(s):  
HELMUTH HÜFFEL
Keyword(s):  
Field Theory ◽  
Particle System ◽  
Relativistic Particle ◽  
Point Particle ◽  
Quantization Scheme ◽  
Stochastic Quantization ◽  
Quantization Method ◽  
Second Quantization ◽  
Spinning Particle ◽  
Constrained Hamiltonian Systems

After a brief review of the BRST formalism and of the Parisi-Wu stochastic-quantization method, the BRST-stochastic-quantization scheme is introduced. This scheme allows the second quantization of constrained Hamiltonian systems in a manifestly gauge-symmetry-preserving way. The examples of the relativistic particle, the spinning particle and the bosonic string are worked out in detail. The paper is closed with a discussion on the interacting field theory associated with the relativistic-point-particle system.

Semiclassical Form of the Relativistic Particle Propagator

1997 ◽  
Vol 12 (32) ◽  
pp. 2435-2443
Author(s):  
Dmitri M. Gitman ◽  
Stoian I. Zlatev
Keyword(s):  
Electromagnetic Field ◽  
Relativistic Particle ◽  
External Electromagnetic Field ◽  
Path Integral Representation ◽  
Constant Electromagnetic Field ◽  
Final Formula ◽  
Nonrelativistic Quantum Mechanics ◽  
Van Vleck ◽  
Detailed Derivation ◽  
Particle Propagator

A detailed derivation of the semiclassical form for the relativistic particle propagator in arbitrary external electromagnetic field is presented. To this end a path-integral representation is used. The final formula is a generalization of the Van Vleck–Pauli–Morette semiclassical representation in the nonrelativistic quantum mechanics. We demonstrate the efficiency of the former in the case of an arbitrary constant electromagnetic field.

scholarly journals Spinning relativistic particle in an external electromagnetic field

1997 ◽  
Vol 236 (3) ◽  
pp. 188-192 ◽  
Author(s):  
M Chaichian ◽  
R González Felipe ◽  
D Louis Martinez
Keyword(s):  
Electromagnetic Field ◽  
Relativistic Particle ◽  
External Electromagnetic Field

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.

RELATIVISTIC PARTICLE IN ELECTROMAGNETIC FIELDS WITH A GENERALIZED UNCERTAINTY PRINCIPLE

2012 ◽  
Vol 27 (15) ◽  
pp. 1250080 ◽  
Author(s):  
M. MERAD ◽  
F. ZEROUAL ◽  
M. FALEK
Keyword(s):  
Electromagnetic Field ◽  
Small Parameter ◽  
Uncertainty Principle ◽  
Relativistic Particle ◽  
Generalized Uncertainty Principle ◽  
Limit Case ◽  
Energy Eigenvalues ◽  
Dirac Equations ◽  
Klein Gordon ◽  
Uniform Electromagnetic Field

In this paper, we propose to solve the relativistic Klein–Gordon and Dirac equations subjected to the action of a uniform electromagnetic field with a generalized uncertainty principle in the momentum space. In both cases, the energy eigenvalues and their corresponding eigenfunctions are obtained. The limit case is then deduced for a small parameter of deformation.

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.

MASSLESS POINT PARTICLE WITH RIGIDITY

1989 ◽  
Vol 04 (09) ◽  
pp. 837-847 ◽  
Author(s):  
M.S. PLYUSHCHAY
Keyword(s):  
Relativistic Particle ◽  
Translational Motion ◽  
Point Particle ◽  
Quantum States ◽  
Helical Line ◽  
Classical Motion ◽  
Gauge Invariant ◽  
Velocity Of Light ◽  
Momentum Direction

The model of relativistic particle with rigidity whose action A=−α∫ kds depends on the curvature of particle world trajectory k, is studied. The classical motion of the particle is shown to go along a helical line at superrelativistic velocity and its translational motion along the momentum direction—at the velocity of light (c). After quantization, the parameter a becomes integer, α=n, n>0. The quantum states of the system are massless states of helicities λ=n and λ=−n in which the evolution of gauge-invariant coordinate occurs at velocity c.

Sign in / Sign up

Export Citation Format

Share Document