Hamiltonian Formulation of the Pilot-Wave Theory

Dan N. Vollick

Published 2021-01-21Version 1

In the pilot-wave theory of quantum mechanics particles have definite positions and velocities and the system evolves deterministically. The velocity of a particle is determined by the wave function of the system (the guidance equation) and the wave function evolves according to Schrodinger's equation. In this paper I first construct a Hamiltonian that gives Schrodinger's equation and the guidance equation for the particle. I then find the Hamiltonian for a relativistic particle in Dirac's theory and for a quantum scalar field.