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arXiv · 1111.7043

The Stochastic Representation of Hamiltonian Dynamics and The Quantization of Time

Matthew F. Brown
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Abstract

Here it is shown that the unitary dynamics of a quantum object may be obtained as the conditional expectation of a counting process of object-clock interactions. Such a stochastic process arises from the quantization of the clock, and this is derived naturally from the matrix-algebra representation of the nilpotent Newton-Leibniz time differential [Belavkin]. It is observed that this condition expectation is a rigorous formulation of the Feynman Path Integral.

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Matthew F. Brown. 2011-11-30. The Stochastic Representation of Hamiltonian Dynamics and The Quantization of Time. https://arxiv.org/abs/1111.7043

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