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

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.

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- Mathematical Physics
- 51 Physical sciences
- 49 Mathematical sciences
- 02 Physical Sciences
- 01 Mathematical Sciences

### Citation

*Journal of Mathematical Physics*,

*26*(9), 2239–2256. https://doi.org/10.1063/1.526803

*Journal of Mathematical Physics*26, no. 9 (January 1, 1985): 2239–56. https://doi.org/10.1063/1.526803.

*Journal of Mathematical Physics*, vol. 26, no. 9, Jan. 1985, pp. 2239–56.

*Scopus*, doi:10.1063/1.526803.

## Published In

## DOI

## ISSN

## Publication Date

## Volume

## Issue

## Start / End Page

## Related Subject Headings

- Mathematical Physics
- 51 Physical sciences
- 49 Mathematical sciences
- 02 Physical Sciences
- 01 Mathematical Sciences