Phase space path integrals, coherent states and Wiener measure. (English) Zbl 0731.60107

Daubechies, I.

Functional integration methods in stochastic quantum mechanics, Proc. Jt. Concordia-Sherbrooke Semin. Ser., Sherbrooke & Montréal/Québec (Can.) 1987, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 25, 157-176 (1991).

Summary: [For the entire collection see Zbl 0722.00045.]
We define the phase space path integral for a one-dimensional quantum particle with Hamiltonian H, give its coherent state interpretation, and show how this path integral can be made rigorous by introducing a Wiener measure and taking the limit as the diffusion constant for the associated diffusion process tends to infinity.

MSC:

60K40	Other physical applications of random processes
81Q30	Feynman integrals and graphs; applications of algebraic topology and algebraic geometry

Keywords:

phase space path integral; coherent state interpretation; Wiener measure

Citations:

Zbl 0722.00045