Fermion Systems in Discrete Space-Time

TL;DR

This paper introduces a model of fermion systems in discrete space-time, using a permutation-symmetric variational principle that leads to spontaneous symmetry breaking and the emergence of a discrete causal structure.

Contribution

It proposes a novel variational principle for fermions in discrete space-time that explains the emergence of causal structure through spontaneous symmetry breaking.

Findings

Fermion systems can be modeled with a permutation-symmetric variational principle.

Minimizers of the principle spontaneously break permutation symmetry.

Discrete causal structure emerges from the fermion interactions.

Abstract

Fermion systems in discrete space-time are introduced as a model for physics on the Planck scale. We set up a variational principle which describes a non-local interaction of all fermions. This variational principle is symmetric under permutations of the discrete space-time points. We explain how for minimizers of the variational principle, the fermions spontaneously break this permutation symmetry and induce on space-time a discrete causal structure.