We evaluate the noncommutative Chern-Simons action induced by fermions interacting with an Abelian gauge field in a noncommutative massive Thirring model in (2+1)-dimensional spacetime. This calculation is performed in the Dirac and Majorana representations. We observe that in the Majorana representation when $\overline{\theta }$ goes to zero we do not have an induced Chern-Simons term in the dimensional regularization scheme.

• Received 5 May 2003

DOI:https://doi.org/10.1103/PhysRevD.68.087701