Conformal Groups in Geometry and Spin Structures
Conformal Groups in Geometry and Spin Structures By Pierre Anglès
English | PDF | 2008 | 307 Pages | ISBN : 0817635122 | 12.19 MB
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.
* 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
* 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.