On Global Properties of Quantum Systems
Consider a smooth connected manifold M and a physical system which is “based” on M (configuration space), i.e. one can localize the system in a sufficiently large class of regions U M and observe how the localization region moves. The properties of such a system will depend on the geometry of M. Its description may be based in a natural manner on those objects on M, which are characteristic for its structure, like compactly supported functions, n-forms, vector fields,jets, etc. Special examples are Hamiltonian systems , non-relativistic quantum systems on homogeneous spaces ,  and Maxwell fields on manifolds , .
KeywordsConfiguration Space Global Property Selfadjoint Operator Selfadjoint Extension Position Projection
Unable to display preview. Download preview PDF.
- 1.R. Abraham and J.E. Marsden, “Foundation of Mechanics”, 2 nd edition, Benjamin (1978)Google Scholar
- 2.R.W. Machey, “Induced Representations and Quantum Mechanics”, Benjamin, New York (1968)Google Scholar
- 9.M. Kac, see e.g. B. Booß, “Topologie und Analysis”, Springer, Berlin (1977)Google Scholar
- 11.J. Petry, “Proceedings of the Conference on Differentialgeometric Methods in Mathematical Physics, Clausthal, 1978, to be published in ”Lecture Notes in Physics“, Springer, Berlin (1980)Google Scholar
- 12.H.D. Doebner, J. Tolar in preparationGoogle Scholar
- 14.F. Pasemann, Proceedings of the Conference on Differentialgeometric Methods in Mathematical Physics, Clausthal, 1978, to be published in “Lecture Notes in Physics”, Springer, Berlin (1980)Google Scholar
- 15.H. Snellman, Ann. Inst. Henri Poincaré, A24: 393 (1976)Google Scholar
- 16.S.T. Hu, “Homology Theory’; Holden-Day, San Francisco (1970)Google Scholar
- 17.J.M. Jauch, “Foundations of Quantum Mechanics”, Addison-Wesley, Reading, Mass. (1968)Google Scholar