Noncommutative Spacetime in Very Special Relativity

Abstract

Very Special Relativity (VSR) framework, proposed by Cohen and Glashow [1], demonstrated that a proper subgroup of the Poincaré group, (in particular ISIM(2)), is sufficient to describe the spacetime symmetries of the so far observed physical phenomena. Subsequently a deformation of the latter, $DISI{M}_b(2)$, was suggested by Gibbons, Gomis and Pope [2]. In the present work, we introduce a novel Non-Commutative (NC) spacetime structure, underlying the $DISI{M}_b(2)$. This allows us to construct explicitly the $DISI{M}_b(2)$ generators, consisting of a sector of Lorentz rotation generators and the translation generators. Exploiting the Darboux map technique, we construct a point particle Lagrangian that lives in the NC phase space proposed by us and satisfies the modified dispersion relation proposed by Gibbons et. al. [2]. It is interesting to note that in our formulation the momentum algebra becomes non-commutative.

15 pages, no figures, change in Title and Abstract, paper completely rewritten, no change in mathematical results and conclusion; to appear in Phys. Lett. A

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