Three Easy Pieces (in tribute to Roman Jackiw)

TL;DR

This paper presents three simple models illustrating advanced concepts in topological physics, magnetic monopoles, and fractional quantum numbers, inspired by Roman Jackiw's influential work.

Contribution

It introduces three novel, minimalistic systems demonstrating complex topological and quantum phenomena, expanding understanding of these concepts in accessible models.

Findings

Topological surface structures in materials

Shape-space magnetic monopole in mechanical systems

Fractional angular momentum in quantum molecules

Abstract

Roman Jackiw has made highly original and influential contributions to several areas of physics that have grown and blossomed, notably including the quantum physics of domain walls, magnetic monopoles, and fractional quantum numbers. Here I offer three small pieces that take off from those themes. I discuss the emergence of topological surface structure in materials, the emergence of a shape-space magnetic monopole in a simple mechanical system, and the emergence of fractional angular momentum in an even simpler quantum mechanical (molecular) system.