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Quantum-mechanical path integrals with Wiener measure for all polynomials Hamiltonians. II. (English) Zbl 0979.81517
Summary: The coherent-state representation of quantum-mechanical propagators as well-defined phase-space path integrals involving Wiener measure on continuous phase-space paths in the limit that the diffusion constant diverges is formulated and proved. This construction covers a wide class of selfadjoint Hamiltonians, including all those which are polynomials in the Heisenberg operators; in fact, this method also applies to maximal symmetric Hamiltonians that do not possess a selfadjoint extension. This construction also leads to a natural covariance of the path integral under canonical transformations. An entirely parallel discussion for spin variables leads to the representation of the propagator for an arbitrary spin-operator Hamiltonian as well-defined path integrals involving Wiener measure on the unit sphere, again in the limit that the diffusion constant diverges.

MSC:
81S40 Path integrals in quantum mechanics
81S30 Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics
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