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Quantum Poincaré-Cartan integral invariant for singular system. (Chinese. English summary) Zbl 1140.81406

Summary: In order to study the symmetry of a singular system, based on a phase-space generation of the Green function of a singular system with finite degrees of freedom, an integral invariant of quantum Poincaré-Cartan type (excluding ground state denoted by \(|0>\)) is established. The relationship between the Poincaré-Cartan integral invariant and the Hamilton-Jacobi equation is discussed at the quantum level. It is pointed that the Hamilton-Jacobi equation can be deduced from integral invariant of the quantum Poincaré-Cartan type.

MSC:

81Q99 General mathematical topics and methods in quantum theory
70H20 Hamilton-Jacobi equations in mechanics
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