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Wick rotation for quantum field theories on degenerate Moyal space(-time). (English) Zbl 1280.81136

Summary: In this paper the connection between quantum field theories on flat noncommutative space(-times) in Euclidean and Lorentzian signature is studied for the case that time is still commutative. By making use of the algebraic framework of quantum field theory and an analytic continuation of the symmetry groups which are compatible with the structure of Moyal space, a general correspondence between field theories on Euclidean space satisfying a time zero condition and quantum field theories on Moyal Minkowski space is presented (“Wick rotation”). It is then shown that field theories transferred to Moyal space(-time) by Rieffel deformation and warped convolution fit into this framework, and that the processes of Wick rotation and deformation commute.{
©2013 American Institute of Physics}

MSC:

81T75 Noncommutative geometry methods in quantum field theory
81R15 Operator algebra methods applied to problems in quantum theory
58B34 Noncommutative geometry (à la Connes)
44A35 Convolution as an integral transform
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