Ebook: Supersymmetry for mathematicians. An introduction

Just as ordinary symmetries relate various forms of matter to each other, and various basic forces to each other, so the novel concept of supersymmetry relates (Fermi) matter to (Bose) force. It is the aim of this book to provide a brief introductory description of the new physical and mathematical ideas involved in formulating supersymmetric theories. The book starts with a physical motivation of supersymmetry, a presentation of the mathematics of Lie superalgebras, supergroups and superspace. Techniques for constructing manifestly globally supersymmetric field theories are given, using the superfield formalism. To allow for a clear flow of ideas, the basic ideas and techniques are worked out in low space dimensionalities where the formulae do not obscure the concepts. Generalizations to four space-time dimensions are then readily come by. Some quantum aspects are discussed. Possible phenomenological applications are not emphasized. Supergravities, locally supersymmetric theories are then considered in 4 and 11 dimensions, in component formalism. An introduction to supersymmetry will be of interest to postgraduate students and researchers in theoretical and particle physics, especially those working in quantum field theory, quantum gravity, general relativity and supergravity. The book will also be of interest to mathematicians with an interest in theoretical physics "This book presents the foundations of supersymmetry to the mathematically minded reader in a cogent and self-contained manner. It begins with a brief introduction to the physical foundations of the theory, especially the classification of relativistic particles and their wave equations, such as the equations of Dirac and Weyl. It then continues the development of the theory of supermanifolds stressing the analogy with the Grothendieck theory of schemes. All the super linear algebra needed for the book is developed here and the basic theorems are established: differential and integral calculus in supermanifolds, Frobenius theorem, foundations of the theory of super Lie groups, and so on.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."--BOOK JACKET.  Read more... Chapter 2. The Concept of a Supermanifold 59 -- Chapter 3. Super Linear Algebra 83 -- Chapter 4. Elementary Theory of Supermanifolds 127 -- Chapter 5. Clifford Algebras, Spin Groups, and Spin Representations 169 -- Chapter 6. Fine Structure of Spin Modules 211 -- Chapter 7. Superspacetimes and Super Poincare Groups 273