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arXiv · hep-th/0602009

DSR Relativistic Particle in a Lagrangian formulation and Non-Commutative Spacetime: A Gauge Independent Analysis

Subir Ghosh
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Abstract

In this paper we have constructed a coordinate space (or geometric) Lagrangian for a point particle that satisfies the Doubly Special Relativity (DSR) dispersion relation in the Magueijo-Smolin framework. At the same time, the symplectic structure induces a Non-Commutative phase space, which interpolates between $κ$-Minkowski and Snyder phase space. Hence this model bridges an existing gap between two conceptually distinct ideas in a natural way. We thoroughly discuss how this type of construction can be carried out from a phase space (or first order) Lagrangian approach. The inclusion of external physical interactions are also briefly outlined. The work serves as a demonstration of how Hamiltonian (and Lagrangian) dynamics can be built around a given non-trivial symplectic structure.

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Subir Ghosh. 2007-03-12. DSR Relativistic Particle in a Lagrangian formulation and Non-Commutative Spacetime: A Gauge Independent Analysis. https://doi.org/10.1016/j.physletb.2007.03.016

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