Christoph Dehne (Leipzig):

On the path integral in non-commutative QFT

Abstract:

Recently, quantum field theories on non-commutative spacetimes have developed into a domain of intensive theoretical research. Mostly, they are constructed from ordinary quantum field theory by introducing star products and turn out to be effectively nonlocal. In the case of time/space non-commutativity, we show within the Hamiltonian approach how this nonlocality leads to an ambiguity in the set-up of the path integral formula. The resulting Feynman rules are therefore different (already at tree level !). In particular, we explain how they correspond to different time-orderings (causal versus covariant). Finally, we comment on further aspects like Wick rotation, the relation between (reflexion) positivity and the (famous) UV/IR connection.

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