Pilot-wave quantum theory in discrete space and time and the principle of least action

Abstract

The idea of obtaining a pilot-wave quantum theory on a lattice with discrete time is presented. The motion of quantum particles is described by a $|\Psi {|}^2$-distributed Markov chain. Stochastic matrices of the process are found by the discrete version of the least-action principle. Probability currents are the consequence of Hamilton's principle and the stochasticity of the Markov process is minimized. As an example, stochastic motion of single particles in a double-slit experiment is examined.

9 pages, 7 figs, accepted for publication in Foundations of Physics

References in corpus (5)

• Bohmian Mechanics and Quantum Field Theory
• On Galilean and Lorentz invariance in pilot-wave dynamics
• Quantum Hamiltonians and Stochastic Jumps
• A proposal for a Bohmian ontology of quantum gravity
• Bell's Jump Process in Discrete Time

Cited by in corpus (1)

• Pilot-Wave Simulator: Exact Classical Sampling from Ideal and Noisy Quantum Circuits up to Hundreds of Qubits