Noncommutative relativistic particles

Abstract

We present a relativistic formulation of noncommutative mechanics where the object of noncommutativity ${\ensuremath{\theta}}^{\ensuremath{\mu}\ensuremath{\nu}}$ is considered as an independent quantity. Its canonical conjugate momentum is also introduced so that it permits one to obtain an explicit form for the generators of the extended Poincar\'e 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.