The Minkowski and Conformal Superspaces

The Classical and Quantum Descriptions

This book is aimed at graduate students and researchers in physics and mathematics who seek to understand the basics of supersymmetry from a mathematical point of view. It provides a bridge between the physical and mathematical approaches to the superworld. The physicist who is devoted to learning the basics of supergeometry can find a friendly approach here, since only the concepts that are strictly necessary are introduced. On the other hand, the mathematician who wants to learn from physics will find that all the mathematical assumptions are firmly rooted in physical concepts. This may open up a channel of communication between the two communities working on different aspects of supersymmetry.

Starting from special relativity and Minkowski space, the idea of conformal space and superspace is built step by step in a mathematically rigorous way, and always connecting with the ideas and notation used in physics. While the book is mainly devoted to these important physical examples of superspaces, it can also be used as an introduction to the field of supergeometry, where a reader can ease into the subject without being overwhelmed with the technical difficulties.

Contents:

• Introduction to Supergeometry

• The Ordinary Minkowski and Conformal Spaces

• Supersymmetry in Physics

• The Minkowski and Conformal Superspaces

• Deformations of the Minkowski and Conformal Superspaces

• Appendices:

  • Categories
  • Representability Criterion
  • Lie Superalgebras and Lie Supergroups of Classical Type
  • Super Harish-Chandra Pairs
  • Quantum Supergroups

Readership: Graduate students and researchers in mathematics and physics interested in supersymmetry.
Key Features:

• Comprehensible introduction to supergeometry: why the algebraic geometric framework is essential
• The superspaces chosen in this book allow us to introduce gradually concepts such as supergroups and homogeneous superspaces while, at the same time working out particular cases that are, both, non-trivial from a mathematical point of view and very important from the physical point of view
• A further step is taken towards non-commutative geometry, although not introducing all its machinery: already at the level of quantum deformation the problem is involved and interesting. The construction may well show a path towards the formulation of physical theories on quantum spaces