Hamiltonian Formulation of the Pilot-Wave Theory

TL;DR

This paper develops a Hamiltonian framework for the pilot-wave theory, linking the guidance equation and Schrödinger's equation, and extends it to relativistic particles and quantum fields.

Contribution

It introduces a Hamiltonian formulation of the pilot-wave theory and generalizes it to relativistic particles and quantum scalar fields.

Findings

Hamiltonian reproduces Schrödinger's and guidance equations

Extended Hamiltonian to Dirac's relativistic theory

Applied Hamiltonian approach to quantum scalar fields

Abstract

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.