A New Action of NC Field Theory with Lorentz Symmetry: -- Application to Gauge Theories --

Abstract

We propose a new action of non-commutative (NC) field theory with Lorentz symmetry, which is obtained by assuming that the NC parameter transforms like an anti-symmetric second-rank tensor, as in the Doplicher-Fredenhagen-Roberts algebra. It is shown that the new action is formally obtained by deleting the 'explicit' dependence of fields on the NC parameter in the Lorentz-invariant Carlson-Carone-Zobin action without vitiating the applicability of 0-expansion in NC gauge theory and thus is identical to that assumed in a previous paper. This confirms our previous calculations in several field theory models, including Lorentz-invariant spinor NCQED, to formulate NC regularization. The present paper continues the application of this method to scalar NCQED and NC U(N) Yang-Mills with Lorentz symmetry. Considering our previous results, we conclude that the new action can be used to define a quantum field theory on NC space-time, at least in the one-loop approximation, which satisfies the correspondence principle in that it has a smooth commutative limit at the level of Feynman diagrams.