**Courant Lecture Notes**

Volume: 11;
2004;
300 pp;
Softcover

MSC: Primary 58; 17; 22;
Secondary 14; 32

Print ISBN: 978-0-8218-3574-6

Product Code: CLN/11

List Price: $46.00

Individual Member Price: $36.80

**Electronic ISBN: 978-1-4704-3111-2
Product Code: CLN/11.E**

List Price: $46.00

Individual Member Price: $36.80

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#### Supplemental Materials

# Supersymmetry for Mathematicians: An Introduction

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*V. S. Varadarajan*

A co-publication of the AMS and the Courant Institute of Mathematical Sciences at New York University

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 well-known mathematician, V. S. Varadarajan, this
book presents a cogent and self-contained exposition of the
foundations of supersymmetry for the mathematically-minded 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 in-depth
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 Harish-Chandra: A Celebration of Representation Theory
and Harmonic Analysis,
The Selected Works of V.S. Varadarajan, and
Algebra in Ancient and Modern
Times.

Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.

#### Table of Contents

# Table of Contents

## Supersymmetry for Mathematicians: An Introduction

- Cover Cover11
- List of editors ii3
- Title page iii4
- Contents v6
- Preface vii8
- Introduction 110
- The concept of a supermanifold 5968
- Super linear algebra 8392
- Elementary theory of supermanifolds 127136
- Clifford algebras, spin groups, and spin representations 169178
- Fine structure of spin modules 211220
- Superspacetimes and super Poincaré groups 273282
- Back Cover Back Cover1311

#### Readership

Graduate students and research mathematicians interested in the mathematical theory of supersymmetry