Observation-based symmetry breaking measures

TL;DR

This paper introduces a general method to quantify symmetry breaking in physical systems through measurable coupling strengths, enabling broader analysis of phase transitions, dynamics, and hidden symmetries.

Contribution

It presents a novel, measurement-based framework for quantifying symmetry breaking applicable across various physical systems.

Findings

Measures can be computed from experimental coupling data

Applicable to diverse physics contexts like phase transitions and hidden symmetries

Provides a quantitative link between symmetry breaking and physical effects

Abstract

Symmetry is one of the most general and useful concepts in physics. A theory or a system that has a symmetry is fundamentally constrained by it. The same constraints do not apply when the symmetry is broken. The quantitative determination of "how much a system breaks a symmetry" allows to reach beyond this binary situation and is a necessary step towards the quantitative connection between symmetry breaking and its effects. We introduce measures of symmetry breaking for a system interacting with external fields (particles). They can be computed from measurements of the system-mediated coupling strengths between subspaces of incoming and outgoing fields (particles) that transform in a definite way under the symmetry. The generality of these symmetry breaking measures and their tight connection to experimental measurements make them applicable to a very wide range of physics, like quantification of phase transitions, constraints in dynamical evolution, and the search for hidden symmetries.