Gauge theory on a quantum phase space. (English) Zbl 0977.81065
Summary: In this letter we present a operator formulation of gauge theories in a quantum phase space which is specified by an operator algebra. For simplicity we work with the Heisenberg algebra. We introduce the notion of the derivative (transport) and Wilson line (parallel transport) which enables us to construct a gauge theory in a simple way. We illustrate the formulation by a discussion of the Higgs mechanism and comment on the large \(N\) masterfield.
MSC:
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
| 81T05 | Axiomatic quantum field theory; operator algebras |
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