Noncommutative massive Thirring model in three-dimensional spacetime
F.A. Brito, T. Mariz, J.R.S. Nascimento, R.F. Ribeiro
TL;DR
This paper investigates the noncommutative massive Thirring model in (2+1) dimensions, focusing on the induced Chern-Simons action from fermion interactions with gauge fields, highlighting differences between Dirac and Majorana representations.
Contribution
It provides the first detailed calculation of the noncommutative Chern-Simons action in this model, revealing representation-dependent effects and the behavior as noncommutativity parameter approaches zero.
Findings
Induced Chern-Simons term appears in Dirac representation.
No induced Chern-Simons term in Majorana representation as θ approaches zero.
The calculation distinguishes effects in different fermion representations.
Abstract
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 Majorana representation when goes to zero we do not have induced Chern-Simons term in the dimensional regularization scheme.
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