## Abstract

We formulate scalar field theories in a curved braided

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

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.

*L*_{∞}-algebra formalism and analyse theircorrelation 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*_{∞}-structure, and we confirm the absence of UV/IR mixing. The calculations of higherloop 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.

Original language | English |
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Publisher | arXiv |

Publication status | Published - 4 Jun 2024 |

## Keywords

- hep-th
- math-ph
- math.MP
- math.QA