BCS as Foundation and Inspiration: The Transmutation of Symmetry

TL;DR

This paper explores how the concepts of pairing and symmetry transmutation from BCS theory have influenced various fields like QCD and quantum statistics, highlighting recent developments and future directions.

Contribution

It provides an overview of the evolution and application of symmetry transmutation ideas beyond traditional superconductivity, emphasizing recent advances in related areas.

Findings

Symmetry transmutation plays a crucial role in modern physics.

Recent developments connect BCS ideas to QCD and quantum statistics.

Future research directions involve exploring symmetry transmutation further.

Abstract

The BCS theory injected two powerful ideas into the collective consciousness of theoretical physics: pairing and spontaneous symmetry breaking. In the 50 years since the seminal work of Bardeen, Cooper, and Schrieffer, those ideas have found important use in areas quite remote from the stem application to metallic superconductivity. This is a brief and eclectic sketch of some highlights, emphasizing relatively recent developments in QCD and in the theory of quantum statistics, and including a few thoughts about future directions. A common theme is the importance of symmetry {\it transmutation}, as opposed to the simple {\it breaking} of electromagnetic $U(1)$ symmetry in classic metallic superconductors.