Conformal Groups in Geometry and Spin Structures

This book provides a self-contained overview of the role of conformal groups in geometry and mathematical physics. It features a careful development of the material, from the basics of Clifford algebras to more advanced topics. Each chapter covers a specific aspect of conformal groups and conformal spin geometry. All major concepts are introduced and followed by detailed descriptions and definitions, and a comprehensive bibliography and index round out the work.

Rich in exercises that are accompanied by full proofs and many hints, the book will be ideal as a course text or self-study volume for senior undergraduates and graduate students.

Conformal groups play a key role in geometry and spin structures. This book provides a self-contained overview of this important area of mathematical physics, beginning with its origins in the works of Cartan and Chevalley and progressing to recent research in spinors and conformal geometry.

Key topics and features:

• Focuses initially on the basics of Clifford algebras

• Studies the spaces of spinors for some even Clifford algebras

• Examines conformal spin geometry, beginning with an elementary study of the conformal group of the Euclidean plane

• Treats covering groups of the conformal group of a regular pseudo-Euclidean space, including a section on the complex conformal group

• Introduces conformal flat geometry and conformal spinoriality groups, followed by a systematic development of riemannian or pseudo-riemannian manifolds having a conformal spin structure

• Discusses links between classical spin structures and conformal spin structures in the context of conformal connections

• Examines pseudo-unitary spin structures and pseudo-unitary conformal spin structures using the Clifford algebra associated with the classical pseudo-unitary space

• Ample exercises with many hints for solutions

• Comprehensive bibliography and index

This text is suitable for a course in mathematical physics at the advanced undergraduate and graduate levels. It will also benefit researchers as a reference text.

Contenu
Classic Groups: Clifford Algebras, Projective Quadrics, and Spin Groups.- Real Conformal Spin Structures.- Pseudounitary Conformal Spin Structures.