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The Batalin-Vilkovisky formalism and the BRST cohomology: a geometric perspectiveÀ venir
Fokko du Cloux (Institut Camille Jordan)
Fokko du Cloux
Institut Camille Jordan
Université Lyon 1,
21 av. Claude Bernard,
The BV construction was first discovered in the context of the quantization of gauge theories via the path integral approach. However, lately this construction has drawn the attention also for its rich mathematical structure.
After a brief introduction on the BV formalism in the context of finite dimensional gauge theories, we will explain how noncommutative geometry, with the notion of noncommutative manifold, provides an interesting mathematical framework for the BV formalism, allowing for a (noncommutative) geometric interpretation of the different elements entering the construction, such as fields/ghost fields, bosons/fermions.
In the second part, we will analyse the BRST cohomology in this finite dimensional setting and, by introducing a notion of generalized Lie algebra cohomology, we will allow the BRST complex for a new description, able to detect a double complex structure, encoding the bosonic/fermionic content of the ghost sector.