Noncommutative relativistic particle on the electromagnetic background

A noncommutative version of D-dimensional relativistic particle is proposed. We consider the particle interacting with the configuration space variable theta(munu)(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 a manifest form. Consistent coupling of NC relativistic particle to the electromagnetic field is constructed and discussed. (C) 2003 Published by Elsevier Science B.V.