The Spinorial Chessboard

ISBN-13: 9783540190783 / Angielski / Miękka / 1988 / 128 str.

Paolo Budinich; Andrzej Trautman

Opis

Spinor theory is an important tool in mathematical physics in particular in the context of conformal field theory and string theory. These lecture notes present a new way to introduce spinors by exploiting their intimate relationship to Clifford algebras. The presentation is detailed and mathematically rigorous. Not only students but also researchers will welcome this book for the clarity of its style and for the straightforward way it applies mathematical concepts to physical theory.

Spis treści

1. Introduction.- 1.1 A Little History.- 1.2 Null Elements and Simple Spinors.- 1.3 About the Present Work.- 1.4 Motivation and Outlook.- 2. Notation and Terminology.- 3. Vector Spaces and Inner Products.- 3.1 Complex Structure in a Real Vector Space.- 3.2 Quaternionic Structure in a Real Vector Space.- 3.3 Complex Conjugation and Hermitean Forms.- 3.4 Real and Quaternionic Structures in a Complex Vector Space.- 3.5 Inner Products in Vector Spaces.- 4. Algebras and Their Representations.- 4.1 Definitions.- 4.2 Simple Algebras.- 4.3 Antiautomorphisms and Inner Products.- 4.4 Real Algebras.- 4.5 Graded Algebras.- 5. General Properties of Clifford Algebras.- 5.1 Definition and General Properties of Clifford Algebras.- 5.2 The Vector Space Structure of Clifford Algebras.- 5.3 The Graded Structure of Clifford Algebras.- 5.4 The Volume Element and Hodge Duality.- 5.5 Relation Between the Clifford Algebras of Vector Spaces of Adjacent Dimension.- 6. Complex Clifford Algebras.- 6.1 Dirac and Weyl Spinors.- 6.2 The Inner Products.- 6.3 Extensions of Representations.- 6.4 The Wall Groups.- 7. Real Clifford Algebras.- 7.1 The Index Periodicity.- 7.2 Charge Conjugation and Majorana Spinors.- 7.3 The Dirac Forms.- 7.4 Clifford Algebras of Euclidean Spaces.- 7.5 The Spinorial Chessboard.- 7.6 Summary.- References.