Effective constraints for quantum systems. (English) Zbl 1167.81025
Summary: An effective formalism for quantum constrained systems is presented which allows manageable derivations of solutions and observables, including a treatment of physical reality conditions without requiring full knowledge of the physical inner product. Instead of a state equation from a constraint operator, an infinite system of constraint functions on the quantum phase space of expectation values and moments of states is used. The examples of linear constraints as well as the free non-relativistic particle in parametrized form illustrate how standard problems of constrained systems can be dealt with in this framework.
MSC:
81S10 | Geometry and quantization, symplectic methods |
53D17 | Poisson manifolds; Poisson groupoids and algebroids |
81S30 | Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics |
References:
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