On fermion grading symmetry

TL;DR

This paper investigates the univalence superselection rule, examining whether fermion grading symmetry can be spontaneously broken in infinite lattice models, and discusses the theoretical necessity of its unbreakability.

Contribution

It provides a rigorous analysis of fermion grading symmetry, supporting the univalence superselection rule in the context of infinite lattice models.

Findings

Fermion grading symmetry cannot be spontaneously broken in physical models.

The study clarifies the theoretical status of fermion grading symmetry.

Supports the univalence superselection rule as fundamental.

Abstract

We consider the univalence superselection rule. One would say perhaps ``There is no indication in nature to invalidate this rule. Fermions do not condensate!'' To explain our motivation, let us recall the correspondence of fermion systems and Pauli systems by the Jordan-Wigner transformation. For a finite lattice, fermion grading symmetry corresponds to the Pauli grading. For an infinite lattice, the Pauli-grading can be spontaneously broken e.g. for the XY-model. What is the status of the fermion grading? Nature tells that fermion grading symmmetry cannot be broken for any physical model. But it seems that its rigorous support is needed.