Quantum-mechanical path integrals with Wiener measure for all polynomial Hamiltonians. II

Journal Article (Journal Article)

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 self-adjoint 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 self-adjoint 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. © 1985 American Institute of Physics.

Full Text

Duke Authors

Cited Authors

  • Daubechies, I; Klauder, JR

Published Date

  • January 1, 1985

Published In

Volume / Issue

  • 26 / 9

Start / End Page

  • 2239 - 2256

International Standard Serial Number (ISSN)

  • 0022-2488

Digital Object Identifier (DOI)

  • 10.1063/1.526803

Citation Source

  • Scopus