The E(2) Particle

Abstract

Recently it has been advocated [1] that for describing nature within the minimal symmetry requirement, certain subgroups of Lorentz group may play a fundamental role. One such group is E(2) which induces a Lie algebraic Non-Commutative spacetime [4] where translation invariance is not fully maintained. We have constructed a consistent structure of Non-commutative phase space for this system and furthermore we have studied an appropriate point particle action on it. Interestingly, the Einstein dispersion relation $p^2=m^2$ remains intact. The model is constructed by exploiting a dual canonical phase space following the scheme developed by us earlier [8].

Latex, 15 pages, revised version, references added, to appear in Phys.Rev.D

References in corpus (18)

• Quantum Gravity at a Lifshitz Point
• Membranes at Quantum Criticality
• Very Special Relativity
• General Very Special Relativity is Finsler Geometry
• The General Very Special Relativity in Finsler Cosmology
• Deformed Special Relativity and Deformed Symmetries in a Canonical Framework
• Acceleration-Extended Galilean Symmetries with Central Charges and their Dynamical Realizations
• A Lagrangian for DSR Particle and the Role of Noncommutativity
• Deformed Symmetry in Snyder Space and Relativistic Particle Dynamics
• A Realization of the Cohen-Glashow Very Special Relativity
• The Free Particle in Deformed Special Relativity
• A Lorentz-Violating Origin of Neutrino Mass?
• DSR Relativistic Particle in a Lagrangian formulation and Non-Commutative Spacetime: A Gauge Independent Analysis
• The Relativistic Particle: Dirac observables and Feynman propagator
• Dirac Quantization Condition for Monopole in Noncommutative Space-Time
• Obtaining the equation of motion for a fermionic particle in a generalized Lorentz-violating system framework
• Dirac neutrino mass from the beta decay end-point modified by the dynamics of a Lorentz-violating equation of motion
• An Arena for Model Building in the Cohen-Glashow Very Special Relativity

Cited by in corpus (4)

• Imperfect fluids, Lorentz violations and Finsler Cosmology
• Noncommutative Spacetime in Very Special Relativity
• Relativistic Particles on Quantum Space-time
• Very special relativity as particle in a gauge field and two-time physics