Interacting fermion dynamics in Majorana phase-space

TL;DR

This paper develops a phase-space approach using Majorana fermions and the Q-function to analyze fermion dynamics, deriving a generalized Fokker-Planck equation with implications for quantum measurement and stochastic processes.

Contribution

It introduces a Majorana-based fermionic phase-space representation and derives a generalized Fokker-Planck equation applicable to various fermionic Hamiltonians.

Findings

Derived a traceless diffusion term in the Fokker-Planck equation

Established a stochastic process interpretation of fermion dynamics

Connected the approach to quantum measurement theory

Abstract

The problem of fermion dynamics is studied using the Q-function for fermions. This is a probabilistic phase-space representation, which we express using Majorana operators, so that the phase-space variable is a real antisymmetric matrix. We consider a general interaction Hamiltonian with four Majorana operators and arbitrary properties. Our model includes the Majorana Hubbard and Fermi Hubbard Hamiltonians, as well as general quantum field theories of interacting fermions. Using the Majorana Q-function we derive a generalized Fokker-Planck equation, with results for the drift and diffusion terms. The diffusion term is proved to be traceless, which gives a dynamical interpretation as a forwards-backwards stochastic process. This approach leads to a model of quantum measurement in terms of an ontology with real vacuum fluctuations.