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

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 $\kappa$-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.

9 pages, LaTex, Title and abstract changed, Thoroughly revised version, No major change in conclusions, Title modified, sign typos in eq.s corrected, to appear in PLB

References in corpus (4)

• A Lagrangian for DSR Particle and the Role of Noncommutativity
• Deformed Symmetry in Snyder Space and Relativistic Particle Dynamics
• The Free Particle in Deformed Special Relativity
• Can an odd number of fermions be created due to chiral anomaly?

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