Fermion Systems in Discrete Space-Time Exemplifying the Spontaneous Generation of a Causal Structure

TL;DR

This paper investigates fermion systems in discrete space-time models, demonstrating how spontaneous symmetry breaking can lead to the emergence of a causal structure through analytical and numerical methods.

Contribution

It introduces a novel approach to modeling space-time at the Planck scale using fermion systems with few particles, highlighting spontaneous symmetry breaking as a mechanism for causal structure emergence.

Findings

Spontaneous symmetry breaking occurs in the models.

Discrete causal structures emerge from the fermion systems.

Analytical and numerical methods confirm the phenomenon.

Abstract

As toy models for space-time on the Planck scale, we consider examples of fermion systems in discrete space-time which are composed of one or two particles defined on two up to nine space-time points. We study the self-organization of the particles as described by a variational principle both analytically and numerically. We find an effect of spontaneous symmetry breaking which leads to the emergence of a discrete causal structure.