1111.7043 (Matthew F. Brown)

The Stochastic Representation of Hamiltonian Dynamics and The
Quantization of Time    [PDF]

Matthew F. Brown

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.

View original: http://arxiv.org/abs/1111.7043