Perturbative effective action for the photon in noncommutative QED2 and exactness of the Schwinger mass

Abstract

In this paper, we discuss the noncommutative QED2 in the S-matrix framework. We are interested in perturbatively proving that the exact Schwinger mass μ2 ¼ e2 π does not receive noncommutative corrections to any order in loop expansion. In this sense, the S-matrix approach is useful since it allows us to work with the effective action Γ½A (interaction term) to compute the corresponding gauge field 1PI two-point function at higher orders. Furthermore, by means of α-cohomology, we generalize the QED2 S-matrix analysis in the Moyal star product to all translation-invariant star products.