Mathematical Foundations of Supersymmetry (Ems Series of Lectures in Mathematics)

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 Fr?©chet space in the super context. A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society. 1. Z/2z-graded Linear Algebra -- 2. Sheaves, Functors And The Geometric Point Of View -- 3. Supergeometry -- 4. Differentiable Supermanifolds -- 5. The Local Structure Of Morphisms -- 6. The Frobenius Theorem -- 7. Super Lie Groups -- 8. Actions Of Super Lie Groups -- 9. Homogeneous Spaces -- 10. Supervarieties And Superschemes -- 11. Algebraic Supergroups. Claudio Carmeli, Lauren Caston, Rita Fioresi. Includes Bibliographical References.