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In this talk, two different strands of quantum field theory on non-commutative space will be presented. First, the scattering of the quantized Dirac field on Minkowski spacetime will be discussed, and it will be explained how this gives rise to observables of the quantized Dirac field on Moyal-deformed Minkowski spacetime. Furthermore, it will be argued that this construction is a model for obtaining a correspondence between more general Lorentzian non-commutative geometries in the sense of spectral geometry and observables of quantum field theories over such non-commutative Lorentzian geometries. In the second strand of the talk, the problem of Wick rotation, i.e. the relation between a quantum field theory on Euclidean space on one hand, and Minkowski spacetime on the other, will be generalized for the Moyal deformations of Euclidean space and Minkowski spacetime. It will be shown that there is a relation if the Moyal deformation leaves the time coordinate untouched. These latter results were obtained in joint work with H. Grosse, G. Lechner and T. Ludwig.

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Rainer Verch, Universität Leipzig
Seminarraum Theoretische Physik
Contact: not specified