The Stochastic Representation of Hamiltonian Dynamics and The Quantization of Time

2011/11/30 by Brown, Matthew F.
#81P05 #FOS: Physical sciences #History and Philosophy of Physics (physics.hist-ph) #Mathematical Physics (math-ph) #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.1111.7043

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.

Related

• Time as a stochastic process
• The Stochastic-Quantum Theorem
• Classical stochastic representation of quantum mechanics
• The Stochastic-Quantum Correspondence
• The Stochastic-Quantum Correspondence