Quantum constraints. (English) Zbl 1110.81136
Summary: This is a review of the main features of the program of quantum constraints developed by Hurst, Grundling et al. Specifically, we develop the mathematical structures implied by a state selection condition of the type \(\omega(C^*C)=0\) in a \(C^*\)-algebra framework. We consider internal compatibility questions for a constraint set, compatibility conditions of constraints with group actions (and the 3-cocycles arising from implementation issues), and compatibility with space-time locality. For examples, we consider linear bosonic constraints, and Gupta-Bleuler electromagnetism.
MSC:
| 81T05 | Axiomatic quantum field theory; operator algebras |
| 81R15 | Operator algebra methods applied to problems in quantum theory |
| 46L60 | Applications of selfadjoint operator algebras to physics |
| 81-02 | Research exposition (monographs, survey articles) pertaining to quantum theory |
Keywords:
locality; Haag-Kastler axioms; quantum field theory; CCR-algebra; \(C^*\)-algebra; Gupta-Bleuler electromagnetismReferences:
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