Deformed Special Relativity and Deformed Symmetries in a Canonical Framework

TL;DR

This paper presents a canonical phase space approach to Deformed Special Relativity in $$-Minkowski spacetime, revealing a mapping to standard phase space and Lorentz transformations, simplifying the analysis of deformed symmetries and their phenomenological implications.

Contribution

It introduces a canonical phase space framework for $$-Minkowski spacetime that simplifies the understanding of deformed symmetries and transformations in DSR models.

Findings

Mapping to canonical phase space simplifies deformed symmetry analysis.

Constructed deformed symmetry generators with standard algebra.

Demonstrated phenomenological applications in classical and quantum mechanics.

Abstract

In this paper we have studied the nature of kinematical and dynamical laws in $\kappa $-Minkowski spacetime from a new perspective: the canonical phase space approach. We discuss a particular form of $\kappa$-Minkowski phase space algebra that yields the $\kappa$-extended finite Lorentz transformations derived in \cite{kim}. This is a particular form of a Deformed Special Relativity model that admits a modified energy-momentum dispersion law as well as noncommutative $\kappa$-Minkowski phase space. We show that this system can be completely mapped to a set of phase space variables that obey canonical (and {\it{not}} $\kappa$-Minkowski) phase space algebra and Special Relativity Lorentz transformation (and {\it{not}} $\kappa$-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 $\kappa$-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 $\kappa$-particle.