Gauge symmetry breaking in the adiabatic self-consistent collective coordinate method

TL;DR

This paper investigates how gauge symmetry is broken in the adiabatic self-consistent collective coordinate (ASCC) method due to adiabatic approximation and truncation, and explores ways to preserve it with higher-order operators.

Contribution

It analyzes gauge symmetry breaking in the ASCC method caused by adiabatic approximation and proposes including higher-order operators to maintain gauge symmetry.

Findings

Gauge symmetry is partially broken by adiabatic approximation.

Truncation of the adiabatic expansion affects gauge symmetry.

Including higher-order operators can preserve gauge symmetry.

Abstract

We study gauge symmetry breaking by adiabatic approximation in the adiabatic self-consistent collective coordinate (ASCC) method. In the previous study, we found that the gauge symmetry of the equation of collective submanifold is (partially) broken by its decomposition into the three moving-frame equations depending on the order of $p$. In this study, we discuss the gauge symmetry breaking by the truncation of the adiabatic expansion. A particular emphasis is placed on the symmetry under the gauge transformations which are not point transformations. We also discuss a possible version of the ASCC method including the higher-order operators which can keep the gauge symmetry.