Abstract
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 [1], non-relativistic quantum systems on homogeneous spaces [2], [3] and Maxwell fields on manifolds [4], [5].
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© 1980 Plenum Press, New York
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Doebner, H.D., Tolar, J. (1980). On Global Properties of Quantum Systems. In: Gruber, B., Millman, R.S. (eds) Symmetries in Science. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-3833-8_30
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DOI: https://doi.org/10.1007/978-1-4684-3833-8_30
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