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 θμν(τ) instead of the numerical matrix. The corresponding Poincaré invariant action has a local symmetry, which allows one to impose the gauge θ0i=0, θij=const. The matrix θij turns out to be the noncommutativity parameter of the gauge fixed formulation. Poincaré 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.