Deformed special relativity and deformed symmetries in a canonical framework

Subir Ghosh and Probir Pal
Phys. Rev. D 75, 105021 – Published 31 May 2007

Abstract

In this paper we have studied the nature of kinematical and dynamical laws in κ-Minkowski spacetime from a new perspective: the canonical phase space approach. We discuss a particular form of κ-Minkowski phase space algebra that yields the κ-extended finite Lorentz transformations derived in [D. Kimberly, J. Magueijo, and J. Medeiros, Phys. Rev. D 70, 084007 (2004).]. This is a particular form of a deformed special relativity model that admits a modified energy-momentum dispersion law as well as noncommutative κ-Minkowski phase space. We show that this system can be completely mapped to a set of phase space variables that obey canonical (and not κ-Minkowski) phase space algebra and special relativity Lorentz transformation (and not κ-extended Lorentz transformation). The complete set of deformed symmetry generators are constructed that obeys an unmodified closed algebra but induce deformations in the symmetry transformations of the physical κ-Minkowski phase space variables. Furthermore, we demonstrate the usefulness and simplicity of this approach through a number of phenomenological applications both in classical and quantum mechanics. We also construct a Lagrangian for the κ-particle.

  • Received 22 March 2007

DOI:https://doi.org/10.1103/PhysRevD.75.105021

©2007 American Physical Society

Authors & Affiliations

Subir Ghosh

  • Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Calcutta 700108, India

Probir Pal

  • Physics Department, Uluberia College, Uluberia, Howrah 711315, India

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Issue

Vol. 75, Iss. 10 — 15 May 2007

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