Particle Trajectories for Quantum Field Theory

TL;DR

This paper extends Bohmian mechanics to relativistic quantum field theories, providing explicit stochastic trajectories for particles, including creation and annihilation processes, in a lattice bosonic model.

Contribution

It adapts Bell's approach to bosonic quantum fields on a lattice, enabling explicit computation of particle trajectories and dynamics.

Findings

Explicit stochastic trajectories for particles are computed.

Particle creation and annihilation are demonstrated within the model.

The approach is applicable to both massive and massless particles.

Abstract

The formulation of quantum mechanics developed by Bohm, which can generate well-defined trajectories for the underlying particles in the theory, can equally well be applied to relativistic Quantum Field Theories to generate dynamics for the underlying fields. However, it does not produce trajectories for the particles associated with these fields. Bell has shown that an extension of Bohm's approach can be used to provide dynamics for the fermionic occupation numbers in a relativistic Quantum Field Theory. In the present paper, Bell's formulation is adopted and elaborated on, with a full account of all technical detail required to apply his approach to a bosonic quantum field theory on a lattice. This allows an explicit computation of (stochastic) trajectories for massive and massless particles in this theory. Also particle creation and annihilation, and their impact on particle propagation, is illustrated using this model.