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In this paper, we discuss the noncommutative QED2 in the S-matrix framework. We are interested in
perturbatively proving that the exact Schwinger mass Î¼2 Â¼ e2
ï¿½? 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 ï¿½?Â½A (interaction term) to compute the corresponding gauge field 1PI two-point function
at higher orders. Furthermore, by means of Î±-cohomology, we generalize the QED2 S-matrix analysis in
the Moyal star product to all translation-invariant star products.
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