Batalin–Vilkovisky quantization of fuzzy field theories

We apply the modern Batalin–Vilkovisky quantization techniques of Costello and Gwilliam to noncommutative field theories in the finite-dimensional case of fuzzy spaces. We further develop a generalization of this framework to theories that are equivariant under a triangular Hopf algebra symmetry, wh...

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Published in:Letters in mathematical physics 2021-12, Vol.111 (6), Article 149
Main Authors: Nguyen, Hans, Schenkel, Alexander, Szabo, Richard J.
Format: Article
Language:English
Subjects:
Braiding
Complex Systems
Field theory (physics)
Geometry
Group Theory and Generalizations
Mathematical and Computational Physics
Measurement
Physics
Physics and Astronomy
Quantum theory
Scalars
Theoretical
Toruses
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description We apply the modern Batalin–Vilkovisky quantization techniques of Costello and Gwilliam to noncommutative field theories in the finite-dimensional case of fuzzy spaces. We further develop a generalization of this framework to theories that are equivariant under a triangular Hopf algebra symmetry, which in particular leads to quantizations of finite-dimensional analogues of the field theories proposed recently through the notion of ‘braided L ∞ -algebras’. The techniques are illustrated by computing perturbative correlation functions for scalar and Chern–Simons theories on the fuzzy 2-sphere, as well as for braided scalar field theories on the fuzzy 2-torus.
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subjects Braiding
Complex Systems
Field theory (physics)
Geometry
Group Theory and Generalizations
Mathematical and Computational Physics
Measurement
Physics
Physics and Astronomy
Quantum theory
Scalars
Theoretical
Toruses
title Batalin–Vilkovisky quantization of fuzzy field theories
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