Batalin-Vilkovisky quantization with an angular twist

Djordje Bogdanović; Marija Dimitrijević Ćirić; Richard J. Szabo

doi:10.48550/arXiv.2604.16225

Batalin-Vilkovisky quantization with an angular twist

Djordje Bogdanović
, Marija Dimitrijević Ćirić
, Richard J. Szabo

Research output: Working paper › Preprint

Abstract

We construct cubic scalar field theory on λ-Minkowski space by combining the Batalin-Vilkoviskyformalism with harmonic analysis, and produce two inequivalent noncommutative quantum fieldtheories. The braided theory is based on a braided L∞-algebra whereby covariance dictates aspectral decomposition into cylindrical Bessel functions that diagonalise the angular Drinfel’dtwist; in this theory we find the usual logarithmic ultraviolet divergences and confirm the absenceof UV/IR mixing. The standard noncommutative theory is based on a classical L∞-algebra;in this theory we relate the spectral decompositions into plane wave and cylindrical harmoniceigenmodes of the Klein-Gordan operator, we verify the planar equivalence theorem, and wedemonstrate a periodic form of UV/IR mixing in which non-planar correlators are genericallyultraviolet finite but become non-analytic on an infinite lattice of exceptional momenta.

Original language	English
Publisher	arXiv
DOIs	https://doi.org/10.48550/arXiv.2604.16225
Publication status	Published - 17 Apr 2026

Keywords

hep-th
math-ph
math.QA
angular twist
λ-Minkowski space
scalar field theory
BV quantization

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title = "Batalin-Vilkovisky quantization with an angular twist",

abstract = "We construct cubic scalar field theory on λ-Minkowski space by combining the Batalin-Vilkoviskyformalism with harmonic analysis, and produce two inequivalent noncommutative quantum fieldtheories. The braided theory is based on a braided L∞-algebra whereby covariance dictates aspectral decomposition into cylindrical Bessel functions that diagonalise the angular Drinfel{\textquoteright}dtwist; in this theory we find the usual logarithmic ultraviolet divergences and confirm the absenceof UV/IR mixing. The standard noncommutative theory is based on a classical L∞-algebra;in this theory we relate the spectral decompositions into plane wave and cylindrical harmoniceigenmodes of the Klein-Gordan operator, we verify the planar equivalence theorem, and wedemonstrate a periodic form of UV/IR mixing in which non-planar correlators are genericallyultraviolet finite but become non-analytic on an infinite lattice of exceptional momenta.",

keywords = "hep-th, math-ph, math.QA, angular twist, λ-Minkowski space, scalar field theory, BV quantization",

author = "Djordje Bogdanovi{\'c} and {\'C}iri{\'c}, \{Marija Dimitrijevi{\'c}\} and Szabo, \{Richard J.\}",

note = "41 pages",

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month = apr,

day = "17",

doi = "10.48550/arXiv.2604.16225",

language = "English",

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TY - UNPB

T1 - Batalin-Vilkovisky quantization with an angular twist

AU - Bogdanović, Djordje

AU - Ćirić, Marija Dimitrijević

AU - Szabo, Richard J.

N1 - 41 pages

PY - 2026/4/17

Y1 - 2026/4/17

N2 - We construct cubic scalar field theory on λ-Minkowski space by combining the Batalin-Vilkoviskyformalism with harmonic analysis, and produce two inequivalent noncommutative quantum fieldtheories. The braided theory is based on a braided L∞-algebra whereby covariance dictates aspectral decomposition into cylindrical Bessel functions that diagonalise the angular Drinfel’dtwist; in this theory we find the usual logarithmic ultraviolet divergences and confirm the absenceof UV/IR mixing. The standard noncommutative theory is based on a classical L∞-algebra;in this theory we relate the spectral decompositions into plane wave and cylindrical harmoniceigenmodes of the Klein-Gordan operator, we verify the planar equivalence theorem, and wedemonstrate a periodic form of UV/IR mixing in which non-planar correlators are genericallyultraviolet finite but become non-analytic on an infinite lattice of exceptional momenta.

AB - We construct cubic scalar field theory on λ-Minkowski space by combining the Batalin-Vilkoviskyformalism with harmonic analysis, and produce two inequivalent noncommutative quantum fieldtheories. The braided theory is based on a braided L∞-algebra whereby covariance dictates aspectral decomposition into cylindrical Bessel functions that diagonalise the angular Drinfel’dtwist; in this theory we find the usual logarithmic ultraviolet divergences and confirm the absenceof UV/IR mixing. The standard noncommutative theory is based on a classical L∞-algebra;in this theory we relate the spectral decompositions into plane wave and cylindrical harmoniceigenmodes of the Klein-Gordan operator, we verify the planar equivalence theorem, and wedemonstrate a periodic form of UV/IR mixing in which non-planar correlators are genericallyultraviolet finite but become non-analytic on an infinite lattice of exceptional momenta.

KW - hep-th

KW - math-ph

KW - math.QA

KW - angular twist

KW - λ-Minkowski space

KW - scalar field theory

KW - BV quantization

U2 - 10.48550/arXiv.2604.16225

DO - 10.48550/arXiv.2604.16225

M3 - Preprint

BT - Batalin-Vilkovisky quantization with an angular twist

PB - arXiv

ER -

Batalin-Vilkovisky quantization with an angular twist

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Keywords

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