Proceedings of the International Conference on Geometry, Integrability and Quantization

Clifford Algebras and Their Applications to Lie Groups and Spinors

Dmitry Shirokov

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Abstract

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.

Article information

Source
Proceedings of the Nineteenth International Conference on Geometry, Integrability and Quantization, Ivaïlo M. Mladenov and Akira Yoshioka, eds. (Sofia: Avangard Prima, 2018), 11-53

Dates
First available in Project Euclid: 23 December 2017

Permanent link to this document
https://projecteuclid.org/ euclid.pgiq/1513998415

Digital Object Identifier
doi:10.7546/giq-19-2018-11-53

Mathematical Reviews number (MathSciNet)
MR3586156

Citation

Shirokov, Dmitry. Clifford Algebras and Their Applications to Lie Groups and Spinors. Proceedings of the Nineteenth International Conference on Geometry, Integrability and Quantization, 11--53, Avangard Prima, Sofia, Bulgaria, 2018. doi:10.7546/giq-19-2018-11-53. https://projecteuclid.org/euclid.pgiq/1513998415


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