Path-wise stochastic calculus of variations with the classical action and quantum systems

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Abstract
In this paper a quantization procedure is described based on the requirement that the configuration of a quantum system performs a diffusion making stationary the mean classical action with respect to variations of the sample paths. In the path-wise calculus of variations contributions of higher order than in the usual Ito^’s stochastic calculus are analyzed in the estimate of infinitesimal increments of the configuration and of its variations.

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