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arXiv · 2604.16225

Batalin-Vilkovisky quantization with an angular twist

Djordje Bogdanović·Marija Dimitrijević Ćirić·Richard J. Szabo
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Abstract

We construct cubic scalar field theory on $\lambda$-Minkowski space by combining the Batalin-Vilkovisky formalism with harmonic analysis, and produce two inequivalent noncommutative quantum field theories. The braided theory is based on a braided $L_\infty$-algebra whereby covariance dictates a spectral decomposition into cylindrical Bessel functions that diagonalise the angular Drinfel'd twist; in this theory we find the usual logarithmic ultraviolet divergences and confirm the absence of UV/IR mixing. The standard noncommutative theory is based on a classical $L_\infty$-algebra; in this theory we relate the spectral decompositions into plane wave and cylindrical harmonic eigenmodes of the Klein-Gordan operator, we verify the planar equivalence theorem, and we demonstrate a periodic form of UV/IR mixing in which non-planar correlators are generically ultraviolet finite but become non-analytic on an infinite lattice of exceptional momenta.

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Djordje Bogdanović, Marija Dimitrijević Ćirić, Richard J. Szabo. 2026-04-17. Batalin-Vilkovisky quantization with an angular twist. https://arxiv.org/abs/2604.16225

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