Conformal Groups in Geometry and Spin Structures

Pierre Anglès

ISBN 10: 0817635122 / ISBN 13: 9780817635121

Editore: Birkhäuser, Birkhäuser Nov 2007, 2007

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This item is printed on demand - Print on Demand Titel. Neuware -Conformal groups play a key role 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. Its scope and clarity will also appeal to researchers in mathematics and physics.Springer Nature c/o IBS, Benzstrasse 21, 48619 Heek 312 pp. Englisch.

Codice articolo 9780817635121

Dati bibliografici

• Titolo: Conformal Groups in Geometry and Spin Structures
• Editore: Birkhäuser, Birkhäuser Nov 2007
• Data di pubblicazione: 2007
• Lingua: Inglese
• ISBN 10: 0817635122
• ISBN 13: 9780817635121
• Rilegatura: Buch
• Condizione: Neu
• Dimensioni: 241 L x 160 A x 22 P (millimetri) 241 millimetri di larghezza per 160 millimetri di altezza per 22 millimetri di profondità
• Peso: 635 grammi

Descrizione articolo

Riassunto

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:* The first chapter focuses on the basic material on Clifford algebras and spinor spaces, along with the necessary mathematical tools * The second chapter examines conformal spin geometry, starting with an elementary study of the classical conformal group in Euclidean space; it then treats covering groups of the conformal group and includes a section on the complex group * Conformal flat geometry and "conformal spinor groups" are introduced, and the text proceeds through a systematic development of manifolds endowed with conformal spin-structure and the theory of conformal connections* Chapter III covers conformal symplectic geometry and includes a discussion of conformal symplectic flat geometry and the covering groups of the real conformal symplectic group* The final chapter provides a detailed treatment of conformal pseudo-unitary spin structures, with emphasis on projective quadrics and pseudo-Hermitian spaces and their associated Clifford algebrasAll the major aspects of the field are introduced, followed by detailed descriptions and definitions; the books comprehensive index and bibliography give further directions for study and research. Rich in exercises that are accompanied by full proofs and many hints, this work will be ideal as a course text or as a self-study volume for senior undergraduates and graduate students. Its scope and clarity as a reference will also appeal to instructors and researchers in mathematics and physics.

Dalla quarta di copertina

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.