D. S. Shirokov, Clifford algebras and their applications to Lie groups and spinors, URL: https://arxiv.org/abs/1709.06608, (Submitted on 19 Sep 2017 (v1), last revised 20 Jan 2018 (this version, v2))
Abstract: In these lectures, we discuss some well-known facts about Clifford algebras: matrix representations, Cartan’s periodicity of 8, double coverings of orthogonal groups by spin groups, Dirac equation in different formalisms, spinors in n dimensions, etc. We also present our point of view on some problems. Namely, we discuss the generalization of the Pauli theorem, the basic ideas of the method of averaging in Clifford algebras, the notion of quaternion type of Clifford algebra elements, the classification of Lie subalgebras of specific type in Clifford algebra, etc.
Comments: 44 pages
Subjects: Mathematical Physics (math-ph)
MSC classes: 15A66, 22E60, 35Q41
Journal reference: Proceedings of the Nineteenth International Conference on Geometry, Integrability and Quantization, Ivailo M. Mladenov and Akira Yoshioka, eds. (Sofia: Avangard Prima, 2018), 11-53
Source: Email from N. Valous, nek.valous_AT_nct-heidelberg.de, 26 Jan. 2018, https://arxiv.org/abs/1709.06608