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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:

[1] DOI: 10.1142/S0129055X06002772 · Zbl 1124.82010 · doi:10.1142/S0129055X06002772
[2] DOI: 10.1142/S0219887807001941 · Zbl 1168.83308 · doi:10.1142/S0219887807001941
[3] DOI: 10.1088/0264-9381/24/18/015 · Zbl 1128.83044 · doi:10.1088/0264-9381/24/18/015
[4] DOI: 10.1103/PhysRevD.77.023508 · doi:10.1103/PhysRevD.77.023508
[5] DOI: 10.1103/PhysRevD.78.063547 · doi:10.1103/PhysRevD.78.063547
[6] DOI: 10.1103/PhysRevD.70.124022 · doi:10.1103/PhysRevD.70.124022
[7] DOI: 10.1007/BF01225149 · Zbl 0412.58006 · doi:10.1007/BF01225149
[8] DOI: 10.1103/PhysRevD.31.1341 · doi:10.1103/PhysRevD.31.1341
[9] DOI: 10.1007/978-1-4612-1422-9_3 · doi:10.1007/978-1-4612-1422-9_3
[10] DOI: 10.1088/0264-9381/24/3/002 · Zbl 1255.83018 · doi:10.1088/0264-9381/24/3/002
[11] DOI: 10.1103/PhysRevD.75.081301 · doi:10.1103/PhysRevD.75.081301
[12] DOI: 10.1103/PhysRevD.75.123512 · doi:10.1103/PhysRevD.75.123512
[13] DOI: 10.1103/PhysRevD.76.063511 · doi:10.1103/PhysRevD.76.063511
[14] DOI: 10.1007/s10714-008-0645-1 · Zbl 1162.83367 · doi:10.1007/s10714-008-0645-1
[15] DOI: 10.1103/PhysRevD.78.023515 · doi:10.1103/PhysRevD.78.023515
[16] DOI: 10.1088/0264-9381/25/13/135013 · Zbl 1149.81317 · doi:10.1088/0264-9381/25/13/135013
[17] DOI: 10.1142/S0129055X0300176X · Zbl 1076.53103 · doi:10.1142/S0129055X0300176X
[18] DOI: 10.1103/PhysRevD.19.2908 · doi:10.1103/PhysRevD.19.2908
[19] DOI: 10.1088/0264-9381/19/10/313 · Zbl 1008.83037 · doi:10.1088/0264-9381/19/10/313
[20] DOI: 10.4310/ATMP.2003.v7.n2.a2 · doi:10.4310/ATMP.2003.v7.n2.a2
[21] Bojowald M., Living Rev. Relativity 8 pp 11–
[22] DOI: 10.1007/s10714-007-0495-2 · Zbl 1145.83015 · doi:10.1007/s10714-007-0495-2
[23] DOI: 10.1088/0264-9381/23/22/006 · Zbl 1111.83015 · doi:10.1088/0264-9381/23/22/006
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