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Softcover ISBN:  9780821835746 
Product Code:  CLN/11 
List Price:  $49.00 
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AMS Member Price:  $39.20 
eBook ISBN:  9781470431112 
Product Code:  CLN/11.E 
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AMS Member Price:  $36.80 
Softcover ISBN:  9780821835746 
eBook ISBN:  9781470431112 
Product Code:  CLN/11.B 
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Book DetailsCourant Lecture NotesVolume: 11; 2004; 300 ppMSC: Primary 58; 17; 22; Secondary 14; 32;
Supersymmetry has been studied by theoretical physicists since the early 1970s. Nowadays, because of its novelty and significance—in both mathematics and physics—the issues it raises attract the interest of mathematicians.
Written by the wellknown mathematician, V. S. Varadarajan, this book presents a cogent and selfcontained exposition of the foundations of supersymmetry for the mathematicallyminded reader. It begins with a brief introduction to the physical foundations of the theory, in particular, to the classification of relativistic particles and their wave equations, such as those of Dirac and Weyl. It then continues with the development of the theory of supermanifolds, stressing the analogy with the Grothendieck theory of schemes. Here, Varadarajan develops all the super linear algebra needed for the book and establishes the basic theorems: differential and integral calculus in supermanifolds, Frobenius theorem, foundations of the theory of super Lie groups, and so on. A special feature is the indepth treatment of the theory of spinors in all dimensions and signatures, which is the basis of all supergeometry developments in both physics and mathematics, especially in quantum field theory and supergravity.
The material is suitable for graduate students and mathematicians interested in the mathematical theory of supersymmetry. The book is recommended for independent study.
For other wonderful titles written by this author see: Euler through Time: A New Look at Old Themes, The Mathematical Legacy of HarishChandra: A Celebration of Representation Theory and Harmonic Analysis, The Selected Works of V.S. Varadarajan, and Algebra in Ancient and Modern Times.ReadershipGraduate students and research mathematicians interested in the mathematical theory of supersymmetry

Table of Contents

Chapters

Chapter 1. Introduction

Chapter 2. The concept of a supermanifold

Chapter 3. Super linear algebra

Chapter 4. Elementary theory of supermanifolds

Chapter 5. Clifford algebras, spin groups, and spin representations

Chapter 6. Fine structure of spin modules

Chapter 7. Superspacetimes and super Poincaré groups


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Supersymmetry has been studied by theoretical physicists since the early 1970s. Nowadays, because of its novelty and significance—in both mathematics and physics—the issues it raises attract the interest of mathematicians.
Written by the wellknown mathematician, V. S. Varadarajan, this book presents a cogent and selfcontained exposition of the foundations of supersymmetry for the mathematicallyminded reader. It begins with a brief introduction to the physical foundations of the theory, in particular, to the classification of relativistic particles and their wave equations, such as those of Dirac and Weyl. It then continues with the development of the theory of supermanifolds, stressing the analogy with the Grothendieck theory of schemes. Here, Varadarajan develops all the super linear algebra needed for the book and establishes the basic theorems: differential and integral calculus in supermanifolds, Frobenius theorem, foundations of the theory of super Lie groups, and so on. A special feature is the indepth treatment of the theory of spinors in all dimensions and signatures, which is the basis of all supergeometry developments in both physics and mathematics, especially in quantum field theory and supergravity.
The material is suitable for graduate students and mathematicians interested in the mathematical theory of supersymmetry. The book is recommended for independent study.
For other wonderful titles written by this author see: Euler through Time: A New Look at Old Themes, The Mathematical Legacy of HarishChandra: A Celebration of Representation Theory and Harmonic Analysis, The Selected Works of V.S. Varadarajan, and Algebra in Ancient and Modern Times.
Graduate students and research mathematicians interested in the mathematical theory of supersymmetry

Chapters

Chapter 1. Introduction

Chapter 2. The concept of a supermanifold

Chapter 3. Super linear algebra

Chapter 4. Elementary theory of supermanifolds

Chapter 5. Clifford algebras, spin groups, and spin representations

Chapter 6. Fine structure of spin modules

Chapter 7. Superspacetimes and super Poincaré groups