Supersymmetry For Mathematicians An Introduction

An special feature of the book is the treatment in depth of the theory of spinors in all dimensions and signatures, which is the basis of all developments of supergeometry both in physics and mathematics, especially in quantum field theory and supergravity."--Jacket.

An special feature of the book is the treatment in depth of the theory of spinors in all dimensions and signatures, which is the basis of all developments of supergeometry both in physics and mathematics, especially in quantum field theory and supergravity."--Jacket.

A brief introductory description of the new physical and mathematical ideas involved in formulating supersymmetric theories. The basic ideas are worked out in low space dimensionalities and techniques where the formulae do not obscure the concepts.

Supersymmetry is a highly active area of considerable interest among physicists and mathematicians. It is not only fascinating in its own right, but there is also indication that it plays a fundamental role in the physics of elementary particles and gravitation. The purpose of the book is to lay down the foundations of the subject, providing the reader with a comprehensive introduction to the language and techniques, as well as detailed proofs and many clarifying examples. This book is aimed ideally at second-year graduate students. After the first three introductory chapters, the text is divided into two parts: the theory of smooth supermanifolds and Lie supergroups, including the Frobenius theorem, and the theory of algebraic superschemes and supergroups. There are three appendices. The first introduces Lie superalgebras and representations of classical Lie superalgebras, the second collects some relevant facts on categories, sheafification of functors and commutative algebra, and the third explains the notion of Frechet space in the super context.

Supersymmetry is a highly active area of considerable interest among physicists and mathematicians. It is not only fascinating in its own right, but there is also indication that it plays a fundamental role in the physics of elementary particles and gravitation. The purpose of the book is to lay down the foundations of the subject, providing the reader with a comprehensive introduction to the language and techniques, with a special attention to giving detailed proofs and many clarifying examples. It is aimed ideally at a second year graduate student. After the first three introductory chapters, the text divides into two parts: the theory of smooth supermanifolds and Lie supergroups, including the Frobenius theorem, and the theory of algebraic superschemes and supergroups. There are three appendices, the first introducing Lie superalgebras and representations of classical Lie superalgebras, the second collecting some relevant facts on categories, sheafification of functors and commutative algebra, and the third explaining the notion of Fréchet space in the super context.

A run-away bestseller from the moment it hit the market in late 1999. This impressive, thick softcover offers mathematicians and mathematical physicists the opportunity to learn about the beautiful and difficult subjects of quantum field theory and string theory. Cover features an intriguing cartoon that will bring a smile to its intended audience.

Supersymmetry was created by the physicists in the 1970's to give a unified treatment of fermions and bosons, the basic constituents of matter. Since then its mathematical structure has been recognized as that of a new development in geometry, and mathematicians have busied themselves with exploring this aspect. This volume collects recent advances in this field, both from a physical and a mathematical point of view, with an accent on a rigorous treatment of the various questions raised.

This is a set of lecture notes given by the author at the Universities of G”ttingen and Wroclaw. The text presents the axiomatic approach to field theory and studies in depth the concepts of symmetry and supersymmetry and their associated generators, currents and charges. It is intended as a one-semester course for graduate students in the field of mathematical physics and high energy physics.