Noncommutative Time in Quantum Field Theory

Understand

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.