The Stochastic Representation of Hamiltonian Dynamics and The Quantization of Time

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.

21 pages

References in corpus (2)

• A Dynamical Theory of Quantum Measurement and Spontaneous Localization
• Quantum Trajectories, State Diffusion and Time Asymmetric Eventum Mechanics

Cited by in corpus (2)

• Quantum Dynamics, Minkowski-Hilbert space, and A Quantum Stochastic Duhamel Principle
• The Generation of Quantum Hamiltonian Evolution from A Pseudo-Measurement Process