Exceptionality, Supersymmetry and Non-associativity in Physics

TL;DR

This paper reviews the role of exceptional algebraic structures and non-associative algebras in advanced theoretical physics, including quantum mechanics, supergravity, and string theories, highlighting their mathematical and physical significance.

Contribution

It provides an updated overview of how exceptional and non-associative structures appear and are utilized in modern high-energy physics theories.

Findings

Exceptional structures emerge in supergravity and string theories.

Non-associative algebras are relevant in quantum mechanics.

The review emphasizes the mathematical importance of these structures.

Abstract

This is an expanded and updated version of the talk I gave at the meeting organized at CERN on April 27-28, 2015 dedicated to honoring the memory of Bruno Zumino and his legacy. In this talk I review the emergence of exceptional structures and non-associative algebras in quantum mechanics, supergravity and M/superstring theories.