A Lagrangian for DSR Particle and the Role of Noncommutativity

Details A Lagrangian for DSR Particle and the Role of Noncommutativity A Lagrangian for DSR Particle and the Role of Noncommutativity

2006-08-29

arxiv.org/abs/hep-th/0608206v4

Phys.Rev.D74:084019,2006

Physics

High Energy Physics

High Energy Physics - Theory

Minor changes, version to appear in PRD

Scientific paper

10.1103/PhysRevD.74.084019

In this paper we have constructed a coordinate space (or geometric) Lagrangian for a point particle that satisfies the exact Doubly Special Relativity (DSR) dispersion relation in the Magueijo-Smolin framework. Next we demonstrate how a Non-Commutative phase space is needed to maintain Lorentz invariance for the DSR dispersion relation. Lastly we address the very important issue of velocity of this DSR particle. Exploiting the above Non-commutative phase space algebra in a Hamiltonian framework, we show that the speed of massless particles is $c$ and for massive particles the speed saturates at $c$ when the particle energy reaches the maximum value $\kappa $, the Planck mass.

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