Braided Quantum Field Theory

TL;DR

This paper introduces a braided quantum field theory framework on noncommutative spaces with quantum group symmetry, utilizing path integrals and braided Feynman diagrams, and applies it to regularize divergences in $^4$-theory on the quantum 2-sphere.

Contribution

It develops a novel braided quantum field theory approach on noncommutative spaces with quantum group symmetry, including new diagrammatic techniques.

Findings

Braided Feynman diagrams with non-trivial crossings are introduced.

Application to $^4$-theory on the quantum 2-sphere shows divergence regularization.

Framework provides a new way to handle quantum field theories on noncommutative spaces.

Abstract

We develop a general framework for quantum field theory on noncommutative spaces, i.e., spaces with quantum group symmetry. We use the path integral approach to obtain expressions for $n$-point functions. Perturbation theory leads us to generalised Feynman diagrams which are braided, i.e., they have non-trivial over- and under-crossings. We demonstrate the power of our approach by applying it to $\phi^4$-theory on the quantum 2-sphere. We find that the basic divergent diagram of the theory is regularised.