Lagrangian for doubly special relativity particle and the role of noncommutativity

Subir Ghosh
Phys. Rev. D 74, 084019 – Published 18 October 2006

Abstract

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 noncommutative 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 noncommutative 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 κ, the Planck mass.

  • Figure
  • Received 5 September 2006

DOI:https://doi.org/10.1103/PhysRevD.74.084019

©2006 American Physical Society

Authors & Affiliations

Subir Ghosh

  • Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Calcutta 700108, India

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Issue

Vol. 74, Iss. 8 — 15 October 2006

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