Conformal Invariance in noncommutative geometry and mutually interacting Snyder Particles

TL;DR

This paper explores a model of mutually interacting Snyder particles in noncommutative geometry, demonstrating conformal invariance and analyzing the structure of symmetry generators within a novel symplectic framework.

Contribution

It introduces a new interacting Snyder particle model with a coupled Snyder algebra and analyzes its conformal invariance and symmetry structure.

Findings

The model exhibits conformal invariance in noncommutative Snyder geometry.

The Lorentz algebra remains undeformed in the model.

Full conformal algebra requires additional restrictions.

Abstract

A system of relativistic Snyder particles with mutual two-body interaction that lives in a Non-Commutative Snyder geometry is studied. The underlying novel symplectic structure is a coupled and extended version of (single particle) Snyder algebra. In a recent work by Casalbuoni and Gomis, Phys.Rev. D90, 026001 (2014), a system of interacting conventional particles (in commutative spacetime) was studied with special emphasis on it's Conformal Invariance. Proceeding along the same lines we have shown that our interacting Snyder particle model is also conformally invariant. Moreover, the conformal Killing vectors have been constructed. Our main emphasis is on the Hamiltonian analysis of the conformal symmetry generators. We demonstrate that the Lorentz algebra remains undeformed but validity of the full conformal algebra requires further restrictions.