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Group theory in physics. Volume III, Supersymmetries and infinite-dimensional algebras /
Recent devopments, particularly in high-energy physics, have projected group theory and symmetry consideration into a central position in theoretical physics. These developments have taken physicists increasingly deeper into the fascinating world of pure mathematics. This work presents important mat...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
London :
Academic Press,
1989.
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| Colección: | Techniques of physics ;
10. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Front Cover; Supersymmetries and Infinite-Dimensional Algebras; Copyright Page; Preface; Table of Contents; Contents of Volume I; Contents of Volume II; Part D: Lie Superalgebras, Lie Supergroups and their Applications; Chapter 20. Introduction to Superalgebras and Supermatrices; 1 The notion of grading; 2 Associative superalgebras; 3 Grassmann algebras; 4 Supermatrices; Chapter 21. General Properties of Lie Superalgebras; 1 Lie superalgebras introduced; 2 Definitions and immediate consequences; 3 Subalgebras, direct sums and homomorphisms of Lie superalgebras.
- 4 Graded representations of Lie superalgebras5 The adjoint representation and the Killing form of a Lie superalgebra; Chapter 22. Superspace and Lie Supergroups; 1 Grassmann variables as coordinates; 2 Analysis on superspace; 3 Linear Lie supergroups; Chapter 23. The Poincar�e Superalgebras and Supergroups; 1 Introduction; 2 The N = 1, D = 4 Poincar�e superalgebra and supergroup; 3 Extended Poincar�e superalgebras and Poincar�e supergroups for D = 4; 4 The Poincar�e superalgebras and supergroups for Minkowski space-times of general dimension D.
- 5 Irreducible representations of the unextended D = 4 Poincar�e superalgebra6 Irreducible representations of the extended D = 4 Poincar�e superalgebras; 7 Irreducible representations of the Poincar�e superalgebras for general space-time dimensions; Chapter 24. Poincar�e Supersymmetric Fields; 1 Supersymmetric field theory; 2 Supersymmetric multiplets; 3 Superfields; 4 Supersymmetric gauge theories; 5 Spontaneous symmetry breaking; Chapter 25. Simple Lie Superalgebras; 1 An outline of the presentation; 2 The definition of a simple Lie superalgebra and some immediate consequences.
- 3 Classical simple Lie superalgebras4 Graded representations of basic classical simple complex Lie superalgebras; 5 The classical simple real Lie superalgebras; 6 The conformal, de Sitter and anti-de Sitter superalgebras; Part E: Infinite-Dimensional Lie Algebras and Superalgebras and their Applications; Chapter 26. The Structure of Kac-Moody Algebras; 1 Introduction to infinite-dimensional Lie algebras; 2 Construction of Kac-Moody algebras; 3 Properties of general Kac-Moody algebras; 4 Types of complex Kac-Moody algebras; 5 Affine Kac-Moody algebras; 6 Kac-Moody superalgebras.
- Chapter 27. Representations of Kac-Moody Algebras1 Highest weight representations of general Kac-Moody algebras; 2 Highest weight representations of affine Kac-Moody algebras; 3 Character formulae; 4 The vertex construction of the basic representation of a simply laced untwisted affine Kac-Moody algebra; 5 Representations of untwisted affine Kac-Moody algebras in terms of fermion creation and annihilation operators; Chapter 28. The Virasoro Algebra and Superalgebras; 1 The conformal algebras; 2 Representations of the Virasoro algebra.