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Gauge theories on quantum spaces

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arxiv 2210.11890 v1 pith:ANGJHP6J submitted 2022-10-21 hep-th gr-qcmath-phmath.MP

Kilian Hersent , Philippe Mathieu , Jean-Christophe Wallet This is my paper · ORCID
classification hep-thgr-qcmath-phmath.MP
keywords quantumgaugespacesnoncommutativespace-timestheoriesaimingalgebra
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We review the present status of gauge theories built on various quantum space-times described by noncommutative space-times. The mathematical tools and notions underlying their construction are given. Different formulations of gauge theory models on Moyal spaces as well as on quantum spaces whose coordinates form a Lie algebra are covered, with particular emphasis on some explored quantum properties. Recent attempts aiming to include gravity dynamics within a noncommutative framework are also considered.

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  1. A new perspective on non-commutative deformations of field and gauge theories

    hep-th 2026-08 conditional novelty 7.0 of 10

    Star products built from active symmetry transformations give gauge-invariant non-commutative theories under a weakened unimodularity condition, with a planar equivalence theorem keeping internal Feynman structure undeformed.

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