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Roberta Iseppi: The Batalin-Vilkovisky quantization for finite spectral triple
mardi 4 mars 2025, 10:30 - 11:30
Résumé
The Batalin-Vilkovisky (BV) formalism plays a fundamental role in the quantization of gauge theories, yet its rigorous formulation within the framework of noncommutative geometry (NCG) remains an open challenge.
In this talk, I will present recent results solving this problem for U(n)-gauge theories arising from finite spectral triples. A key aspect of the BV construction is the extension of the initial gauge theory through the introduction of ghost fields, which I will formalize using the new notion of BV-spectral triple. I will then discuss how the BV/BRST cohomology complexes naturally align within the NCG framework, establishing connections with appropriate Hochschild complexes.