# THE STOCHASTIC REPRESENTATION OF HAMILTONIAN DYNAMICS AND THE QUANTIZATION OF TIME

@article{Brown2011THESR, title={THE STOCHASTIC REPRESENTATION OF HAMILTONIAN DYNAMICS AND THE QUANTIZATION OF TIME}, author={Matthew F. Brown}, journal={arXiv: Mathematical Physics}, year={2011} }

Here it is shown that the unitary dynamics of a quantum object may be obtained as the expectation of a counting process of object-clock inter- actions. Such a stochastic process arises from the quantization of the clock, and this is derived naturally from the matrix-algebra representation (3) of the nilpo- tent Newton-Leibniz time differential dt. Following (5) we also show that the object-clock interaction dynamics is unitarily equivalent to a pseudo-selfadjoint Schrodinger past-future…

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