A Realization of the Cohen-Glashow Very Special Relativity

Abstract

We show that the Cohen-Glashow Very Special Relativity (VSR) theory [1] can be realized as the part of the Poincaré symmetry preserved on a noncommutative Moyal plane with light-like noncommutativity. Moreover, we show that the three subgroups relevant to the Cohen-Glashow VSR can also be realized in the noncommutative space-time setting. For all these three cases the noncommutativity parameter ${\theta }^{\mu \nu }$ should be light-like (${\theta }^{\mu \nu }{\theta }_{\mu \nu }=0$). A fixed constant noncommutativity parameter respects the T(2) subgroup of Lorentz, while for the E(2) and SIM(2) cases the form of noncommutativity among the coordinates should be of linear (Lie algebra) and quadratic (quantum group) type, respectively. We discuss some physical implications of this realization of the Cohen-Glashow VSR.

5 pages, minor corrections, to appear in Phys. Rev. Lett

References in corpus (5)

• Very Special Relativity
• Twist and Spin-Statistics Relation in Noncommutative Quantum Field Theory
• Noncommutative Quantum Field Theory: A Confrontation of Symmetries
• Noncommutative fields and actions of twisted Poincare algebra
• Twisted Poincaré Symmetry and Some Implications on Noncommutative Quantum Field Theory

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