Statistics, Condensation and the Anderson-Higgs Mechanism: The Worldline Path Integral View

TL;DR

This paper uses a worldline path integral approach to explain the Anderson-Higgs mechanism for bosons and demonstrate its absence for fermions, highlighting the role of worldline supersymmetry.

Contribution

It introduces a novel first quantized path integral formalism with worldline supersymmetry to analyze the Anderson-Higgs effect for both bosons and fermions.

Findings

Higgs effect occurs for charged bosons in a magnetic field

Higgs effect is absent for charged fermions due to worldline supersymmetry

The method provides a unified framework for analyzing exchange statistics and symmetry effects

Abstract

We explain, in the first quantized path integral formalism, the mechanism behind the Anderson-Higgs effect for a gas of charged bosons in a background magnetic field, and then use the method to prove the absence of the effect for a gas of fermions. The exchange statistics are encoded via the inclusion of additional Grassmann coordinates in a manner that leads to a manifest worldline supersymmetry. This extra symmetry is key in demonstrating the absence of the effect for charged fermions.