Constructing measures for path integrals

The overcompleteness of the coherent states for the Heisenberg-Weyl group implies that many different integral kernels can be used to represent the same operator. Within such an equivalence class we construct an integral kernel to represent the quantum-mechanical evolution operator for certain dynamical systems in the form of a path integral that involves genuine (Wiener) measures on continuous phase-space paths. To achieve this goal it is necessary to employ an expression for the classical action different from the usual one. © 1982 American Institute of Physics.

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Author Ingrid Daubechies Mathematics