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 ${\square }^{-1}$ and ${\square }^{-2}$ type. We discuss the meaning of these terms and possible improvements of the model.

29 pages

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