BV quantization of $\phi^3$-theory on $\lambda$-Minkowski space: Tree-level correlation functions

TL;DR

This paper compares standard and braided BV quantization of $$-theory on $$-Minkowski space, analyzing tree-level correlation functions and revealing differences in diagram classes and noncommutative contributions.

Contribution

It introduces a braided BV quantization scheme for $$-theory and compares it with standard quantization, highlighting differences in correlation functions and diagram classes.

Findings

Standard quantization yields two classes of diagrams for the four-point function.

Braided quantization results in a single diagram class with phase-dependent noncommutativity.

The two approaches differ in how noncommutativity influences correlation functions.

Abstract

We review the quantization of scalar field theory on $\lambda$-Minkowski space using the Batalin--Vilkovisky (BV) formalism. We consider $\phi^3$-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.