QUANTUM FIELD THEORY ON NONCOMMUTATIVE SPACE–TIME: THE RELATION BETWEEN ULTRAVIOLET BEHAVIOUR, TOPOLOGY AND SYMMETRY
2001
We study properties of a scalar quantum field theory on two-dimensional noncommutative space–times. We show that ultraviolet behaviour of a field theory on noncommutative spaces is sensitive to the topology of the space–time, namely to its compactness. The compactness of space-like coordinates implies discreteness of the time variable which leads to appearance of unphysical modes and violation of unitarity even in the absence of a star-product in the interaction terms. Thus, this conclusion holds also for other quantum field theories with discrete time.
Keywords:
- Noncommutative algebraic geometry
- Noncommutative quantum field theory
- Thermal quantum field theory
- Quantum electrodynamics
- Quantum gravity
- Relationship between string theory and quantum field theory
- Noncommutative geometry
- Quantum differential calculus
- Physics
- Topology
- Ultraviolet fixed point
- Quantum mechanics
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