FIRST STEPS TOWARDS THE QUANTISATION OF THE SPECTRAL ACTION: THE BATALIN-VILKOVISKY CONSTRUCTION OF FINITE SPECTRAL TRIPLES

Speaker(s)

ROBERTA ISEPPI

Affiliation

Georg-August-Universität Göttingen, Germany

Language of the talk

English

Date

April 16, 2025, 5:15 p.m.

Information about the event

ZOOM

Title in Polish

FIRST STEPS TOWARDS THE QUANTISATION OF THE SPECTRAL ACTION: THE BATALIN-VILKOVISKY CONSTRUCTION OF FINITE SPECTRAL TRIPLES

Seminar

North Atlantic Noncommutative Geometry Seminar

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The quantisation of the spectral action associated with spectral triples remains a largely open problem. Even within a perturbative framework, significant complications arise in the presence of non-abelian gauge symmetries. This is precisely where the Batalin-Vilkovisky (BV) formalism proves useful, offering a powerful tool for handling the divergences that appear in the perturbative quantisation of gauge theories. In this talk, I will explore the possibility of developing a BV quantisation procedure entirely within the context of noncommutative geometry. After briefly reviewing the core ideas behind the BV quantisation, I will present recent progress in this direction, showing how the formalism can be coherently and fully implemented in the language of spectral triples, at least in the finite-dimensional case.

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