Batalin-Vilkovisky quantization with an angular twist
Djordje Bogdanović, Marija Dimitrijević Ćirić, Richard J. Szabo
TLDR
This paper constructs two noncommutative quantum field theories on $λ$-Minkowski space using Batalin-Vilkovisky quantization with an angular twist, analyzing their UV/IR properties.
Key contributions
- Developed two distinct noncommutative QFTs on $λ$-Minkowski space using BV formalism and harmonic analysis.
- The braided theory, based on an $L_\infty$-algebra, shows standard UV divergences and no UV/IR mixing.
- The standard theory confirms planar equivalence and exhibits periodic UV/IR mixing at exceptional momenta.
Why it matters
This work advances our understanding of quantum field theories on noncommutative spacetimes. By comparing two distinct constructions, it sheds light on the presence or absence of UV/IR mixing, a crucial challenge in these theories. This helps in developing more robust and consistent models for quantum gravity.
Original Abstract
We construct cubic scalar field theory on $λ$-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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