Abstract
After arguing why the Batalin–Vilkovisky (BV) formalism is expected to find a natural description within the framework of noncommutative geometry, we explain how this relation takes form for gauge theories induced by finite spectral triples. In particular, we demonstrate how the two extension procedures appearing in the BV formalism, that is, the initial extension via the introduction of ghost/anti-ghost fields and the further extension with auxiliary fields, can be described in the language of noncommutative geometry using the notions of the BV spectral triple and total spectral triple, respectively. The construction is presented in detail for all U(2)-gauge theories induced by spectral triples on the algebra M2(C). Indications are given on how to extend the results to U(n)-gauge theories for n > 2.
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