Wiener measures for quantum mechanical path integrals

John R. Klauder

John R. Klauder

I. V. V. Raghavacharyulu

L. V. Kapitanskii

Ingrid C. Daubechies, John R. Klauder

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.

Kim Young Sik

We investigate the behavior of a Wiener integral along the path of the scale factor as a function of a parameter for the Wiener integral about complex valued measurable function defined on the Wiener space which is frequently used in Quantum Mechanics.