Braided scalar quantum field theory

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.

41 pages; v2: typos corrected; v3: minor changes and typos fixed; v4: Final version to be published in Fortschritte der Physik