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arXiv:quant-ph/0007015 · Journal of Mathematical Physics

Stochastic mechanics and the Feynman integral

Michele Pavon

Published Sep 1, 2000• 15 citations
arXivHTMLPDF

Abstract

The Feynman integral is given a stochastic interpretation in the framework of Nelson’s stochastic mechanics employing a time-symmetric variant of Nelson’s kinematics recently developed by the author.
DOI
10.1063/1.1286880

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A second quantization procedure is formulated in the framework of Nelson’s stochastic mechanics. It is shown that the annihilation operator is given by an integration over a Gaussian white noise Ḃ(s) with the kernel exp(iω(t−s)) and the creation operator is given by an integration over a time reversed Gaussian white noise Ḃ*(s) with the kernel exp(−iω(t−s)). The eigenfunctions on which the operators act are shown to be Gaussian random variables whose collection is dense in a Hilbert space. Employing the above operators, we can construct {N}-representation in the stochastic mechanics.