Finite temperature induced fermion number

TL;DR

This paper investigates how finite temperature affects the fermion number induced by background fields, revealing it becomes non-topological and less sharply defined compared to zero temperature.

Contribution

It demonstrates that finite temperature induces a transition from topological to non-topological fermion number, challenging previous zero-temperature assumptions.

Findings

Finite temperature makes the fermion number non-topological.

The fermion number at finite temperature is not a sharp observable.

Zero temperature fermion number is sensitive only to global properties.

Abstract

The induced fractional fermion number at zero temperature is topological (in the sense that it is only sensitive to global asymptotic properties of the background field), and is a sharp observable (in the sense that it has vanishing rms fluctuations). In contrast, at finite temperature, it is shown to be generically nontopological, and not a sharp observable.