Braided quantum field theory (Q5940444)

This is an attempt to formulate quantum field theory, or at least some of its elements, in the setting of braided categories. From the 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 is regularised.