Deformed Special Relativity and Deformed Symmetries in a Canonical Framework

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.

Revised version with change in Title and Abstract, No change in mathematical content, Reference section enlarged, Discussion on Soccer Ball Problem removed; Version to appear in PRD

References in corpus (3)

• Multi-Particle States in Deformed Special Relativity
• Symplectic geometry and Noether charges for Hopf algebra space-time symmetries
• The Relativistic Particle: Dirac observables and Feynman propagator

Cited by in corpus (7)

• Kappa-Minkowski space-time and the star product realizations
• Twisted Statistics in kappa-Minkowski Spacetime
• Deformed Oscillator Algebras and QFT in $\kappa$-Minkowski Spacetime
• Position-dependent noncommutativity in quantum mechanics
• Rapidities and Observable 3-Velocities in the Flat Finslerian Event Space with Entirely Broken 3D Isotropy
• Black hole evaporation within a momentum-dependent metric
• Local Lorentz Transformation and "Lorentz Violation"