Poincare covariant mechanics on noncommutative space

Abstract

The Dirac approach to constrained systems can be adapted to construct relativistic invariant theories on a noncommutative (NC) space. As an example, we propose and discuss relativistic invariant NC particle coupled to electromagnetic (EM) field by means of the standard term Aμẋ μ. Poincare invariance implies deformation of the free particle NC algebra in the interaction theory. The corresponding corrections survive in the nonrelativistic limit. © SISSA/ISAS 2003.