Braided Quantum Field Theory

Details Braided Quantum Field Theory Braided Quantum Field Theory

1999-06-29

arxiv.org/abs/hep-th/9906225v3

Commun.Math.Phys. 217 (2001) 451-473

Physics

High Energy Physics

High Energy Physics - Theory

31 pages, LaTeX with AMS and XY-Pic macros; final version to appear in Commun. Math. Phys

Scientific paper

10.1007/s002200100375

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.

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