Supersymmetry in physics: an algebraic overview
type: Item
instance of: scholarly article
title: Supersymmetry in physics: an algebraic overview
zbMATH Open document ID: 0578.17001
DOI: 10.1016/0167-2789(85)90146-0
author: B. George
published in: Physica D
publication date: 1985-01-01T00:00:00Z
review text: In December 1983, a conference on ``Supersymmetry in Physics'' was held at Los Alamos. The proceedings were published in Physica D 15 (1985), they provide a valuable overview of this very active field of theoretical physics. The author's lecture surveys some of the uses that finite-dimensional Lie superalgebras might have in physics. He first reviews Kac's list of all complex simple Lie superalgebras. Then he discusses, mainly through various examples, the finite dimensional representations of the so-called classical Lie superalgebras. For non-relativistic applications, all of the Lie superalgebras are potentially useful. On the other hand, the Lie superalgebras which might be applicable in relativistic physics are severely restricted by the principles of special relativity. The author presents, for various space-time dimensions, a list of Lie superalgebras which meet these requirements. Finally, he comments on certain infinite-dimensional representations (those corresponding to massless particles) of some of these relativistic Lie superalgebras.
reviewed by: M. Scheunert
Mathematics Subject Classification ID: 17B81
Mathematics Subject Classification ID: 81T60
Mathematics Subject Classification ID: 17B10
Mathematics Subject Classification ID: 81R05
Mathematics Subject Classification ID: 17-02
Mathematics Subject Classification ID: 81-02
zbMATH DE Number: 3925041
zbMATH Keywords: graded Lie algebras
zbMATH Keywords: finite-dimensional Lie superalgebras
zbMATH Keywords: finite dimensional representations
zbMATH Keywords: classical Lie superalgebras
zbMATH Keywords: infinite-dimensional representations
zbMATH Keywords: relativistic Lie superalgebras
MaRDI profile type: Publication
full work available at URL: 0167-2789(85)90146-0
OpenAlex ID: W2024903627
cites work: Superspace. One thousand and one lessons in supersymmetry. With a foreword by David Pines
cites work: Q3894074
cites work: Classification of all simple graded Lie algebras whose Lie algebra is reductive. II. Construction of the exceptional algebras
cites work: Kac–Dynkin diagrams and supertableaux
cites work: All Possible Symmetries of the S Matrix
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description: scientific article; zbMATH DE number 3925041