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Lorentz invariance, unitarity and UV-finiteness of QFT on noncommutative spacetime. (English) Zbl 1062.81138

Summary: Ultraviolet finite quantum field theory on even-dimensional noncommutative spacetime is formulated using coordinate coherent states. 2D spacetime is foliated into families of orthogonal, noncommutative, two planes. Lorentz invariance is recovered if one imposes a single noncommutative parameter \(\theta\) in the theory. Unitarily is checked at the one-loop level and no violation is found. Being UV finite NCQFT does not present any UV/IR mixing.

MSC:

81T75 Noncommutative geometry methods in quantum field theory
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