Equations of motion on noncompact Hermitian symmetric spaces. (English. Abridged French version) Zbl 0766.35042
Summary: The classical motion and the quantum evolution determined by linear Hamiltonians on coherent state manifolds of noncompact Hermitian symmetric space structure are considered. A matrix Riccati equation, with opposite signs in the quadratic terms in the compact and noncompact cases, determines the classical motion and the quantum evolution. The results are illustrated by the case of the noncompact dual of the complex Grassmann manifold.
MSC:
35Q40 | PDEs in connection with quantum mechanics |
81Q05 | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics |
43A65 | Representations of groups, semigroups, etc. (aspects of abstract harmonic analysis) |