Non-Abelian Magnon Gauge Interactions in Condensed Matter Physics

TL;DR

This paper explores the role of non-Abelian magnon gauge interactions in condensed matter systems, particularly in frustrated magnetic materials and multi-gap magnetic superconductors, highlighting their potential to advance low-energy physics understanding.

Contribution

It introduces theories incorporating non-Abelian magnon gauge interactions to describe complex magnetic phenomena in condensed matter, emphasizing their significance in long-range magnetic order.

Findings

Non-Abelian gauge interactions can describe long-range magnetic order.

Magnon exchange mediates spin-spin interactions in these systems.

Potential implications for understanding non-Abelian condensed matter physics.

Abstract

We discuss three different but closely related theories which could describe varieties of condensed matters, in particular the frustrated magnetic materials and the multi-gap (ferro)magnetic superconductors with or without the photon-magnon mixing, where the genuine non-Abelian magnon gauge interaction plays the central role. The charactristic features of these theories are the existence of long range magnetic order and the spin-spin interaction described by the exchange of the messenger bosons, not by the instantaneous action at a distance. These theories could play important roles in our understanding of non-Abelian condensed matters and make the non-Abelian gauge interaction a main stream in the low energy physics. We discuss the physical implications of our results.