Noncommutative relativistic particles

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.