Braided scalar quantum field theory

TL;DR

This paper develops a braided scalar quantum field theory framework using curved $L_$-algebras, performs detailed two-loop calculations, and introduces new diagrammatic and algebraic tools to analyze correlation functions.

Contribution

It introduces a novel braided $L_$-algebra formalism for scalar fields, along with diagrammatic calculus and algebraic Schwinger-Dyson equations, advancing the mathematical foundation of braided quantum field theories.

Findings

Divergent tadpole contributions are eliminated by a suitable choice of central curvature.

Confirmed the absence of UV/IR mixing in the theory.

Developed a new diagrammatic calculus for higher loop and multiplicity correlator calculations.

Abstract

We formulate scalar field theories in a curved braided $L_\infty$-algebra formalism and analyse their correlation functions using Batalin-Vilkovisky quantization. We perform detailed calculations in cubic braided scalar field theory up to two-loop order and three-point multiplicity. The divergent tadpole contributions are eliminated by a suitable choice of central curvature for the $L_\infty$-structure, and we confirm the absence of UV/IR mixing. The calculations of higher loop and higher multiplicity correlators in homological perturbation theory are facilitated by the introduction of a novel diagrammatic calculus. We derive an algebraic version of the Schwinger-Dyson equations based on the homological perturbation lemma, and use them to prove the braided Wick theorem.