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Title: Electrodynamics of a generalized charged particle in doubly special relativity framework

Abstract

In the present paper, dynamics of generalized charged particles are studied in the presence of external electromagnetic interactions. This particular extension of the free relativistic particle model lives in Non-Commutative κ-Minkowski space–time, compatible with Doubly Special Relativity, that is motivated to describe Quantum Gravity effects. Furthermore we have also considered the electromagnetic field to be dynamical and have derived the modified forms of Lienard–Wiechert like potentials for these extended charged particle models. In all the above cases we exploit the new and extended form of κ-Minkowski algebra where electromagnetic effects are incorporated in the lowest order, in the Dirac framework of Hamiltonian constraint analysis.

Authors:
 [1];  [1];  [2]
  1. Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700 108 (India)
  2. S. N. Bose National Centre for Basic Sciences, Block-JD, Sector-III, Salt Lake, Kolkata 700 098 (India)
Publication Date:
OSTI Identifier:
22314837
Resource Type:
Journal Article
Resource Relation:
Journal Name: Annals of Physics (New York); Journal Volume: 346; Journal Issue: Complete; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ALGEBRA; CHARGED PARTICLES; COMMUTATION RELATIONS; ELECTRODYNAMICS; ELECTROMAGNETIC FIELDS; ELECTROMAGNETIC INTERACTIONS; HAMILTONIANS; LIMITING VALUES; MINKOWSKI SPACE; PARTICLE MODELS; POTENTIALS; QUANTUM GRAVITY; RELATIVISTIC RANGE; RELATIVITY THEORY

Citation Formats

Pramanik, Souvik, E-mail: souvick.in@gmail.com, Ghosh, Subir, E-mail: subir_ghosh2@rediffmail.com, and Pal, Probir, E-mail: probirkumarpal@rediffmail.com. Electrodynamics of a generalized charged particle in doubly special relativity framework. United States: N. p., 2014. Web. doi:10.1016/J.AOP.2014.04.009.
Pramanik, Souvik, E-mail: souvick.in@gmail.com, Ghosh, Subir, E-mail: subir_ghosh2@rediffmail.com, & Pal, Probir, E-mail: probirkumarpal@rediffmail.com. Electrodynamics of a generalized charged particle in doubly special relativity framework. United States. doi:10.1016/J.AOP.2014.04.009.
Pramanik, Souvik, E-mail: souvick.in@gmail.com, Ghosh, Subir, E-mail: subir_ghosh2@rediffmail.com, and Pal, Probir, E-mail: probirkumarpal@rediffmail.com. 2014. "Electrodynamics of a generalized charged particle in doubly special relativity framework". United States. doi:10.1016/J.AOP.2014.04.009.
@article{osti_22314837,
title = {Electrodynamics of a generalized charged particle in doubly special relativity framework},
author = {Pramanik, Souvik, E-mail: souvick.in@gmail.com and Ghosh, Subir, E-mail: subir_ghosh2@rediffmail.com and Pal, Probir, E-mail: probirkumarpal@rediffmail.com},
abstractNote = {In the present paper, dynamics of generalized charged particles are studied in the presence of external electromagnetic interactions. This particular extension of the free relativistic particle model lives in Non-Commutative κ-Minkowski space–time, compatible with Doubly Special Relativity, that is motivated to describe Quantum Gravity effects. Furthermore we have also considered the electromagnetic field to be dynamical and have derived the modified forms of Lienard–Wiechert like potentials for these extended charged particle models. In all the above cases we exploit the new and extended form of κ-Minkowski algebra where electromagnetic effects are incorporated in the lowest order, in the Dirac framework of Hamiltonian constraint analysis.},
doi = {10.1016/J.AOP.2014.04.009},
journal = {Annals of Physics (New York)},
number = Complete,
volume = 346,
place = {United States},
year = 2014,
month = 7
}
  • The aim of this Comment is to call to the attention of double special relativity (DSR) readers a basic fact. The introduction of noncommutative structures in problems like the one addressed by Ghosh [ Phys. Rev. D 74, 084019 (2006)] is not necessary for the understanding of DSR physics. It can be described just as the relativistic free particle problem in a different parametrization.
  • In this paper we have constructed a coordinate space (or geometric) Lagrangian for a point particle that satisfies the exact doubly special relativity (DSR) dispersion relation in the Magueijo-Smolin framework. Next we demonstrate how a noncommutative phase space is needed to maintain Lorentz invariance for the DSR dispersion relation. Lastly we address the very important issue of velocity of this DSR particle. Exploiting the above noncommutative phase space algebra in a Hamiltonian framework, we show that the speed of massless particles is c and for massive particles the speed saturates at c when the particle energy reaches the maximum valuemore » {kappa}, the Planck mass.« less
  • We discuss the definition of velocity as dE/d vertical bar p vertical bar, where E, p are the energy and momentum of a particle, in doubly special relativity (DSR). If this definition matches dx/dt appropriate for the space-time sector, then space-time can in principle be built consistently with the existence of an invariant length scale. We show that, within different possible velocity definitions, a space-time compatible with momentum-space DSR principles cannot be derived.
  • For a certain example of a 'doubly special relativity theory' the modified space-time Lorentz transformations are obtained from the momentum space transformations by using canonical methods. In the sequel an energy-momentum dependent space-time metric is constructed, which is essentially invariant under the modified Lorentz transformations. By associating such a metric to every Planck cell in space and to the energy-momentum contained in it, a solution of the problem of macroscopic bodies in doubly special relativity is suggested.
  • In this article we develop a physical interpretation for the deformed (doubly) special relativity theories (DSRs), based on a modification of the theory of measurement in special relativity. We suggest that it is useful to regard the DSRs as reflecting the manner in which quantum gravity effects induce Planck-suppressed distortions in the measurement of the 'true' energy and momentum. This interpretation provides a framework for the DSRs that is manifestly consistent, nontrivial, and in principle falsifiable. However, it does so at the cost of demoting such theories from the level of fundamental physics to the level of phenomenological models -more » models that should in principle be derivable from whatever theory of quantum gravity one ultimately chooses to adopt.« less