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arXiv · 1101.4798

Noncommutative Time in Quantum Field Theory

Tapio Salminen·Anca Tureanu
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Abstract

We analyze, starting from first principles, the quantization of field theories, in order to find out to which problems a noncommutative time would possibly lead. We examine the problem in the interaction picture (Tomonaga-Schwinger equation), the Heisenberg picture (Yang-Feldman-Källén equation) and the path integral approach. They all indicate inconsistency when time is taken as a noncommutative coordinate. The causality issue appears as the key aspect, while the unitarity problem is subsidiary. These results are consistent with string theory, which does not admit a time-space noncommutative quantum field theory as its low-energy limit, with the exception of light-like noncommutativity.

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Tapio Salminen, Anca Tureanu. 2011-07-19. Noncommutative Time in Quantum Field Theory. https://doi.org/10.1103/physrevd.84.025009

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