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The quantisation of the spectral action for spectral triples remains a largely open problem. Even within a perturbative framework, serious challenges arise when in the presence of non-abelian gauge symmetries. This is precisely where the Batalin–Vilkovisky (BV) formalism comes into play: a powerful tool specifically designed to handle the perturbative quantisation of gauge theories. The central question I will address is whether it is possible to develop a BV formalism entirely within the framework of noncommutative geometry (NCG). After a brief introduction to the key ideas behind BV quantisation, I will report on recent progress toward this goal, showing that the BV formalism can be fully formulated within the language of NCG in the case of finite spectral triples. [-]
The quantisation of the spectral action for spectral triples remains a largely open problem. Even within a perturbative framework, serious challenges arise when in the presence of non-abelian gauge symmetries. This is precisely where the Batalin–Vilkovisky (BV) formalism comes into play: a powerful tool specifically designed to handle the perturbative quantisation of gauge theories. The central question I will address is whether it is possible ...[+]

58B34 ; 81T70 ; 81T13

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An introduction to the BV-BFV formalism - Cattaneo, Alberto S. (Author of the conference) | CIRM H

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The BV-BFV formalism unifies the BV formalism (which deals with the problem of fixing the gauge of field theories on closed manifolds) with the BFV formalism (which yields a cohomological resolution of the reduced phase space of a classical field theory). I will explain how this formalism arises and how it can be quantized.

83C45 ; 81T13 ; 70S05 ; 81T70

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