Quantum fermions and quantum field theory from classical statistics

TL;DR

This paper demonstrates how a classical statistical ensemble, specifically an Ising-type model, can replicate quantum fermion behavior and quantum field theory dynamics, including phenomena like interference and tunneling.

Contribution

It introduces a classical probabilistic framework capable of describing relativistic quantum fermions and their field interactions, bridging classical statistics and quantum field theory.

Findings

Classical probabilities can produce quantum interference and tunneling effects.

The model reproduces the Schrödinger equation in the non-relativistic limit.

A specific law for probability evolution yields quantum fermion dynamics.

Abstract

An Ising-type classical statistical ensemble can describe the quantum physics of fermions if one chooses a particular law for the time evolution of the probability distribution. It accounts for the time evolution of a quantum field theory for Dirac particles in an external electromagnetic field. This yields in the non-relativistic one-particle limit the Schr\"odinger equation for a quantum particle in a potential. Interference or tunneling arise from classical probabilities.