Positivity and topology in lattice gauge theory

TL;DR

This paper discusses the conflict between the admissibility condition used for defining topological charge and the positivity of the transfer matrix in lattice gauge theory.

Contribution

It identifies a fundamental incompatibility between the admissibility condition and the positive transfer matrix in lattice gauge theory.

Findings

Admissibility condition conflicts with transfer matrix positivity

Implications for defining topological charge in lattice gauge theory

Highlights need for alternative approaches

Abstract

The admissibility condition usually used to define the topological charge in lattice gauge theory is incompatible with a positive transfer matrix.