Braided Scalar Quantum Field Theory

We formulate scalar field theories in a curved braided L∞$L_\infty$‐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∞$L_\infty$‐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. We formulate scalar field theories in a curved braided L∞$L_\infty$‐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∞$L_\infty$‐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.