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arXiv · 2406.02372

Braided scalar quantum field theory

Djordje Bogdanović·Marija Dimitrijević Ćirić·Voja Radovanović·Richard J. Szabo·Guillaume Trojani
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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.

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Djordje Bogdanović, Marija Dimitrijević Ćirić, Voja Radovanović, Richard J. Szabo, Guillaume Trojani. 2024-06-04. Braided scalar quantum field theory. https://arxiv.org/abs/2406.02372

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