Lie Particle And Its Batalin-Tyutin Extension

TL;DR

This paper introduces a point particle model that creates a noncommutative three-space with Lie algebraic coordinate brackets, and extends it using Batalin-Tyutin formalism to facilitate quantization.

Contribution

It proposes a novel point particle model with Lie algebraic noncommutative coordinates and embeds it in Batalin-Tyutin extended space for better quantization.

Findings

Model generates a noncommutative space with angular momentum algebra structure.

Embedding in Batalin-Tyutin space yields phase space variables with canonical algebra.

Comparison with previous $ ext{kappa}$-Minkowski models highlights differences.

Abstract

In this Letter we have proposed a point particle model that generates a noncommutative three-space, with the coordinate brackets being Lie algebraic in nature, in particular isomorphic to the angular momentum algebra. The work is in the spirit of our earlier works in this connection, {\it {i.e.}} PLB 618 (2005)243 and PLB 623 (2005)251, where the $\kappa $-Minkowski form of noncomutative spacetime was considered. This non-linear and operatorial nature of the configuration space coordinate algebra can pose problems regarding its quantization. This prompts us to embed the model in the Batalin-Tyutin extended space where the equivalent model comprises of phase space variables satisfying a canonical algebra. We also compare our present model with the point particle model, previously proposed by us, in the context of $\kappa$-Minkowski spacetime.