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Noncommutative relativistic particle

A. A. Deriglazov
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Abstract

Noncommutative version of D-dimensional relativistic particle is proposed. We consider the particle interacting with the configuration space variable $θ^{μν}(τ)$ instead of the numerical matrix. The corresponding Poincare invariant action has a local symmetry, which allows one to impose the gauge $θ^{0i}=0, ~ θ^{ij}=const$. The matrix $θ^{ij}$ turns out to be the noncommutativity parameter of the gauge fixed formulation. Poincare transformations of the gauge fixed formulation are presented in the manifest form.

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A. A. Deriglazov. 2002-07-30. Noncommutative relativistic particle. https://arxiv.org/abs/hep-th/0207274

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