One-loop structure of the U(1) gauge model on the truncated Heisenberg space

Abstract

We calculate divergent one-loop corrections to the propagators of the U(1) gauge theory on the truncated Heisenberg space, which is one of the extensions of the Grosse–Wulkenhaar model. The model is purely geometric, based on the Yang–Mills action; the corresponding gauge-fixed theory is BRST invariant. We quantize perturbatively and, along with the usual wave-function and mass renormalizations, we find divergent nonlocal terms of the □ - 1 and □ - 2 type. We discuss the meaning of these terms and possible improvements of the model.