Noncommutative Time in Quantum Field Theory

Details Noncommutative Time in Quantum Field Theory Noncommutative Time in Quantum Field Theory

2011-01-25

arxiv.org/abs/1101.4798v2

Phys.Rev.D84:025009,2011

Physics

High Energy Physics

High Energy Physics - Theory

25 pages, minor corrections

Scientific paper

10.1103/PhysRevD.84.025009

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-K\"all\'{e}n 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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