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6 - Semisimple Lie Algebras and their Unitary Representations

Published online by Cambridge University Press:  08 December 2022

Esko Keski-Vakkuri ,
Claus Montonen  and
Marco Panero
Esko Keski-Vakkuri
Affiliation:
University of Helsinki
Claus Montonen
Affiliation:
University of Helsinki
Marco Panero
Affiliation:
Università degli Studi di Torino, Italy
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Summary

We introduce the semisimple Lie algebras, discussing their properties and their unitary representations. In particular, we focus on su(N) Lie algebras, which have important applications in elementary particle physics and in condensed matter theory.

Keywords

Lie groupsLie algebrasirreducible representations of Lie algebrasroots and weightssu(N) Lie algebrasYoung tableauxLorentz–Poincaré group
Type
Chapter
Information
Mathematical Methods for Physics
An Introduction to Group Theory, Topology and Geometry
 , pp. 233 - 313
Publisher: Cambridge University Press
Print publication year: 2022

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