Probabilistic cellular automata for interacting fermionic quantum field theories

TL;DR

This paper demonstrates how a classical probabilistic cellular automaton can model an interacting fermionic quantum field theory, reproducing quantum properties and phenomena like symmetry breaking and solitons.

Contribution

It constructs a simple classical automaton for the Thirring model with imaginary coupling, showing quantum mechanics emerges from classical statistical systems.

Findings

The automaton exhibits unitary evolution and quantum properties.

It models phenomena like spontaneous symmetry breaking and solitons.

The model can be analyzed using standard statistical physics techniques.

Abstract

A classical local cellular automaton can describe an interacting quantum field theory for fermions. We construct a simple classical automaton for a particular version of the Thirring model with imaginary coupling. This interacting fermionic quantum field theory obeys a unitary time evolution and shows all properties of quantum mechanics. Classical cellular automata with probabilistic initial conditions admit a description in the formalism of quantum mechanics. Our model exhibits interesting features as spontaneous symmetry breaking or solitons. The same model can be formulated as a generalized Ising model. This euclidean lattice model can be investigated by standard techniques of statistical physics as Monte Carlo simulations. Our model is an example how quantum mechanics emerges from classical statistics.