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Lectures on Clifford algebras and spinors. (Лекции по алгебрам клиффорда и спинорам.) (Russian) Zbl 1291.15063
Lektsionnye Kursy NOTs 19. Moskva: Matematicheskiĭ Institut im. V. A. Steklova, RAN (ISBN 978-5-98419-044-2/pbk). 179 p. (2012).
Clifford algebras are special associative algebras. They can be considered as generalizations of real numbers, complex numbers, and quaternions. The theory of Clifford algebras is closely related to the theory of quadratic forms and orthogonal transformations. Clifford algebras have various applications in many areas of mathematics, physics and engineering. This textbook presents an introduction to Clifford algebras. It is based on eleven lectures given at Steklov Institute of Mathematics in Moscow, Russia. The first five lectures consider basic definitions and properties of real and complex Clifford algebras. Lecture 6 is devoted to the Pauli theorem and its generalizations. The next three lectures examine pseudo-orthogonal groups, Clifford groups and spin groups. Lectures 10 and 11 deal with Dirac, Weyl, Majorana and Majorana-Weyl spinors. Each lecture finishes with suitable examples. In the text, some new results obtained by the author are also presented. Basic information from undergraduate courses on algebra, geometry and topology is included in the appendix. These lecture notes are intended to students and researchers in the field of mathematical physics who know Russian.
MSC:
15A66 Clifford algebras, spinors
11E88 Quadratic spaces; Clifford algebras
15-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to linear algebra
15A75 Exterior algebra, Grassmann algebras
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