Majorana Fermions in Particle Physics, Solid State and Quantum Information

TL;DR

This review explores the multifaceted role of Majorana fermions across particle physics, condensed matter, and quantum computing, highlighting their theoretical origins, diverse applications, and connections to advanced mathematical structures.

Contribution

It provides a comprehensive overview of Majorana fermions' significance and their interdisciplinary implications, emphasizing recent theoretical insights and mathematical relations.

Findings

Majorana fermions have profound implications across multiple physics disciplines.

Connections between Majorana fermions and advanced mathematical structures are elucidated.

The review highlights the ongoing relevance of Majorana fermions in modern physics research.

Abstract

This review is based on lectures given by M. J. Duff summarising the far reaching contributions of Ettore Majorana to fundamental physics, with special focus on Majorana fermions in all their guises. The theoretical discovery of the eponymous fermion in 1937 has since had profound implications for particle physics, solid state and quantum computation. The breadth of these disciplines is testimony to Majorana's genius, which continues to permeate physics today. These lectures offer a whistle-stop tour through some limited subset of the key ideas. In addition to touching on these various applications, we will draw out some fascinating relations connecting the normed division algebras $\mathbb{R}, \mathbb{C}, \mathbb{H}, \mathbb{O}$ to spinors, trialities, $K$-theory and the classification of stable topological states of symmetry-protected gapped free-fermion systems.