DSR Relativistic Particle in a Lagrangian formulation and   Non-Commutative Spacetime: A Gauge Independent Analysis
  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. 
Subir Ghosh (Indian Statistical Institute)