Li, Ruijie; Li, Ziping Quantum Poincaré-Cartan integral invariant for singular system. (Chinese. English summary) Zbl 1140.81406 J. Beijing Univ. Technol. 33, No. 4, 437-440 (2007). 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 Keywords:quantum theory; symmetry; Hamiltonians; Poincaré-Cartan integral invariant PDFBibTeX XMLCite \textit{R. Li} and \textit{Z. Li}, J. Beijing Univ. Technol. 33, No. 4, 437--440 (2007; Zbl 1140.81406)