Spin and Representations

2024/12/06 by Cho, Wonmyeong
#FOS: Mathematics #General Mathematics (math.GM)

paper · doi:10.48550/arxiv.2501.03233

Abstract

We derive the representation theory of SU(2) from the expository theory of Lie groups and Lie algebras. Based on this, the mathematics of non-relativistic quantum mechanics of a spin (1)/(2) particle are described from a representation-theoretic perspective, and are extended to many particle systems.

Related

• Spin operators and representations of the Poincaré group
• Representation theory in the construction of free quantum field
• Potential applications of modular representation theory to quantum mechanics
• The basic physical Lie operations
• The Majorana representation of spins and the relation between SU(∞) and SDiff(S²)