Fermion Systems in Discrete Space-Time - Outer Symmetries and Spontaneous Symmetry Breaking

Abstract

A systematic procedure is developed for constructing fermion systems in discrete space-time which have a given outer symmetry. The construction is illustrated by
simple examples. For the symmetric group, we prove that fermion systems exist only if the number of particles satisfies certain constraints. When applied to physical
systems, this result shows that the permutation symmetry of discrete space-time is always spontaneously broken by the fermionic projector.