Noncommutative relativistic particle

Abstract

Noncommutative version of D-dimensional relativistic particle is proposed. We consider the particle interacting with the configuration space variable ${\theta }^{\mu \nu }(\tau )$ instead of the numerical matrix. The corresponding Poincare invariant action has a local symmetry, which allows one to impose the gauge ${\theta }^{0i}=0,{\theta }^{ij}=const$. The matrix ${\theta }^{ij}$ 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.

5 pages

References in corpus (2)

• Deformation quantization of Poisson manifolds, I
• Open string with a background B-field as the first order mechanics and noncommutativity

Cited by in corpus (6)

• Deformed Symmetry in Snyder Space and Relativistic Particle Dynamics
• Poincare covariant mechanics on noncommutative space
• Noncommutative version of an arbitrary nondegenerated mechanics
• Twisted Space-Time Symmetry, Non-Commutativity and Particle Dynamics
• Theories on noncommutative spaces and deformed symmetries
• Alternative Approach to Noncommutative Quantum Mechanics on a Curved Space