Deformed Symmetry in Snyder Space and Relativistic Particle Dynamics

TL;DR

This paper explores deformed Poincare symmetries in Snyder space, presenting invariant relativistic particle models, deriving Snyder's algebra independently, and relating deformed and usual symmetries.

Contribution

It introduces a gauge-independent derivation of Snyder's algebra from relativistic particle models with deformed symmetries, and discusses an alternative action form.

Findings

Derived Snyder's algebra from particle models independently.

Established relations between deformed and usual symmetries.

Linked particle mass to noncommutativity parameter.

Abstract

We describe the deformed Poincare-conformal symmetries implying the covariance of the noncommutative space obeying Snyder's algebra. Relativistic particle models invariant under these deformed symmetries are presented. A gauge (reparametrisation) independent derivation of Snyder's algebra from such models is given. The algebraic transformations relating the deformed symmetries with the usual (undeformed) ones are provided. Finally, an alternative form of an action yielding Snyder's algebra is discussed where the mass of a relativistic particle gets identified with the inverse of the noncommutativity parameter.