Noncommutative relativistic particles

TL;DR

This paper develops a relativistic noncommutative mechanics framework where the noncommutativity parameter is treated as an independent variable, leading to new Lorentz generators and an extended Klein-Gordon equation.

Contribution

It introduces a relativistic formulation of noncommutative mechanics with independent noncommutativity parameters and derives explicit Lorentz generators.

Findings

Lorentz generators explicitly derived for noncommutative case

Extended Klein-Gordon equation depending on two parameters

Theory invariant under reparametrization

Abstract

We present a relativistic formulation of noncommutative mechanics were the object of noncommutativity $\theta^{\mu\nu}$ is considered as an independent quantity. Its canonical conjugate momentum is also introduced, what permits to obtain an explicit form for the generators of the Lorentz group in the noncommutative case. The theory, which is invariant under reparametrization, generalizes recent nonrelativistic results. Free noncommutative bosonic particles satisfy an extended Klein-Gordon equation depending on two parameters.