BV quantization of $φ^3$-theory on $λ$-Minkowski space: Tree-level correlation functions
Djordje Bogdanović, Marija Dimitrijević Ćirić, Stefan Djordjević, Richard J. Szabo
TLDR
Compares standard and braided BV quantization of $φ^3$-theory on $λ$-Minkowski space, analyzing tree-level correlation functions.
Key contributions
- Compares standard and braided BV quantization for $φ^3$-theory on $λ$-Minkowski space.
- Investigates tree-level three-point and four-point correlation functions.
- Standard BV yields two distinct 4-point diagram classes with varied noncommutativity.
- Braided BV produces a single 4-point diagram class, with noncommutativity as an overall phase.
Why it matters
This paper compares standard and braided BV quantization for $φ^3$-theory on $λ$-Minkowski space. It reveals how different schemes yield distinct correlation function behaviors, crucial for consistent quantum field theories in noncommutative spacetimes.
Original Abstract
We review the quantization of scalar field theory on $λ$-Minkowski space using the Batalin--Vilkovisky (BV) formalism. We consider $φ^3$-theory in two different quantization schemes: standard and braided. While standard BV quantization is based on an ordinary $L_\infty$-algebra, braided BV quantization is based on a braided $L_\infty$-algebra. We compare the tree-level three-point and four-point correlation functions in the two approaches. For the four-point function, standard quantization leads to two inequivalent classes of diagrams with different noncommutative contributions, whereas braided quantization yields only a single class of diagrams with noncommutativity entering solely through an overall phase factor depending on the external momenta.
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