Clifford Algebras and Spinors
Seiten
1997
Cambridge University Press (Verlag)
978-0-521-59916-0 (ISBN)
Cambridge University Press (Verlag)
978-0-521-59916-0 (ISBN)
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Here, Professor Lounesto offers a unique introduction to Clifford algebras and spinors. This will interest physicists as well as mathematicians, and includes treatments of the quantum mechanics of the electron, electromagnetism and special relativity with Clifford algebras.
In this book, Professor Lounesto offers a unique introduction to Clifford algebras and spinors. The beginning chapters could be read by undergraduates; vectors, complex numbers and quaternions are introduced with an eye on Clifford algebras. The next chapters will also interest physicists, and include treatments of the quantum mechanics of the electron, electromagnetism and special relativity with a flavour of Clifford algebras. A new classification of spinors is introduced, one based on bilinear covariants of physical observables. This reveals a new class of spinors, residing between the Weyl, Majorana and Dirac spinors. Scalar products of spinors are classified by involutory anti-automorphisms of Clifford algebras. This leads to the chessboard of automorphism groups of scalar products of spinors. On the algebraic side, Brauer/Wall groups and Witt rings are discussed, and on the analytic, Cauchy's integral formula is generalised to higher dimensions.
In this book, Professor Lounesto offers a unique introduction to Clifford algebras and spinors. The beginning chapters could be read by undergraduates; vectors, complex numbers and quaternions are introduced with an eye on Clifford algebras. The next chapters will also interest physicists, and include treatments of the quantum mechanics of the electron, electromagnetism and special relativity with a flavour of Clifford algebras. A new classification of spinors is introduced, one based on bilinear covariants of physical observables. This reveals a new class of spinors, residing between the Weyl, Majorana and Dirac spinors. Scalar products of spinors are classified by involutory anti-automorphisms of Clifford algebras. This leads to the chessboard of automorphism groups of scalar products of spinors. On the algebraic side, Brauer/Wall groups and Witt rings are discussed, and on the analytic, Cauchy's integral formula is generalised to higher dimensions.
1. Background material; 2. Physical applications; 3. More algebra; 4. Matrix window; 5. Mathematical extensions.
| Erscheint lt. Verlag | 3.7.1997 |
|---|---|
| Reihe/Serie | London Mathematical Society Lecture Note Series |
| Verlagsort | Cambridge |
| Sprache | englisch |
| Maße | 153 x 229 mm |
| Gewicht | 520 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| ISBN-10 | 0-521-59916-4 / 0521599164 |
| ISBN-13 | 978-0-521-59916-0 / 9780521599160 |
| Zustand | Neuware |
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