The Batalin-Vilkovisky (BV) formalism plays a fundamental role in thequantization of gauge theories, yet its rigorous formulation within theframework of noncommutative geometry (NCG) remains an open <a href="http://challenge.
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In this talk, I will present recent results solving this problem forU(n)-gauge theories arising from finite spectral triples. A key aspectof the BV construction is the extension of the initial gauge theorythrough the introduction of ghost fields, which I will formalize usingthe new notion of BV-spectral triple. I will then discuss how theBV/BRST cohomology complexes naturally align within the NCG framework,establishing connections with appropriate Hochschild <a href="http://complexes.

https://indico.math.cnrs.fr/event/13410/ » target= »_blank » title= »complexes.

https://indico.math.cnrs.fr/event/13410/ »>complexes.

https://indico.math.cnrs.fr/event/13410/