James Gaunt
BV quantization of dynamical fuzzy spectral triples
Gaunt, James; Nguyen, Hans; Schenkel, Alexander
Abstract
This paper provides a systematic study of gauge symmetries in the dynamical fuzzy spectral triple models for quantum gravity that have been proposed by Barrett and collaborators. We develop both the classical and the perturbative quantum BV formalism for these models, which in particular leads to an explicit homological construction of the perturbative quantum correlation functions. We show that the relevance of ghost and antifield contributions to such correlation functions depends strongly on the background Dirac operator $D_0$ around which one perturbs, and in particular on the amount of gauge symmetry that it breaks. This will be illustrated by studying quantum perturbations around 1.) the gauge-invariant zero Dirac operator $D_0=0$ in a general $(p,q)$-model, and 2.) a simple example of a non-trivial $D_0$ in the quartic $(0,1)$-model.
Citation
Gaunt, J., Nguyen, H., & Schenkel, A. (2022). BV quantization of dynamical fuzzy spectral triples. Journal of Physics A: Mathematical and Theoretical, 55(47), Article 474004. https://doi.org/10.1088/1751-8121/aca44f
Journal Article Type | Article |
---|---|
Acceptance Date | Nov 18, 2022 |
Online Publication Date | Dec 1, 2022 |
Publication Date | Nov 25, 2022 |
Deposit Date | Dec 7, 2022 |
Publicly Available Date | Dec 7, 2022 |
Journal | Journal of Physics A: Mathematical and Theoretical |
Print ISSN | 1751-8113 |
Electronic ISSN | 1751-8121 |
Publisher | IOP Publishing |
Peer Reviewed | Peer Reviewed |
Volume | 55 |
Issue | 47 |
Article Number | 474004 |
DOI | https://doi.org/10.1088/1751-8121/aca44f |
Keywords | General Physics and Astronomy, Mathematical Physics, Modeling and Simulation, Statistics and Probability, Statistical and Nonlinear Physics |
Public URL | https://nottingham-repository.worktribe.com/output/14305181 |
Publisher URL | https://iopscience.iop.org/article/10.1088/1751-8121/aca44f |
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BV quantization of dynamical fuzzy spectral triples
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Publisher Licence URL
https://creativecommons.org/licenses/by/4.0/
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