Dorje C Brody et al 2009 J. Phys. A: Math. Theor. 42 295303 doi:10.1088/1751-8113/42/29/295303
Metric approach to quantum constraints
Dorje C Brody1, Anna C T Gustavsson2 and Lane P Hughston1
Show affiliationsA framework for deriving equations of motion for constrained quantum systems is introduced and a procedure for its implementation is outlined. In special cases, the proposed new method, which takes advantage of the fact that the space of pure states in quantum mechanics has both a symplectic structure and a metric structure, reduces to a quantum analogue of the Dirac theory of constraints in classical mechanics. Explicit examples involving spin-
particles are worked out in detail: in the first example, our approach coincides with a quantum version of the Dirac formalism, while the second example illustrates how a situation that cannot be treated by Dirac's approach can nevertheless be dealt with in the present scheme.
- PACS
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03.65.Pm Relativistic wave equations
- MSC
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81Q20 Semiclassical techniques including WKB and Maslov methods
81S10 Geometry and quantization, symplectic methods (See also 53D50)
- Subjects
- Dates
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Issue 29 (24 July 2009)
Received 29 April 2009, in final form 10 June 2009
Published 6 July 2009
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Metric approach to quantum constraints
Dorje C Brody et al 2009 J. Phys. A: Math. Theor. 42 295303
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