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TMF, 2013, Volume 175, Number 1, Pages 11–34 (Mi tmf8384)  

This article is cited in 7 scientific papers (total in 7 papers)

Pauli theorem in the description of $n$-dimensional spinors in the Clifford algebra formalism

D. S. Shirokov

Steklov Mathematical Institute, RAS, Moscow, Russia

Abstract: We discuss a generalized Pauli theorem and its possible applications for describing $n$-dimensional (Dirac, Weyl, Majorana, and Majorana–Weyl) spinors in the Clifford algebra formalism. We give the explicit form of elements that realize generalizations of Dirac, charge, and Majorana conjugations in the case of arbitrary space dimensions and signatures, using the notion of the Clifford algebra additional signature to describe conjugations. We show that the additional signature can take only certain values despite its dependence on the matrix representation.

Keywords: Pauli theorem, Clifford algebra, Dirac conjugation, charge conjugation, Majorana conjugation, Majorana–Weyl spinor, Clifford algebra additional signature

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation НШ-2928.2012.1
8215


DOI: https://doi.org/10.4213/tmf8384

Full text: PDF file (603 kB)
References: PDF file   HTML file

English version:
Theoretical and Mathematical Physics, 2013, 175:1, 454–474

Bibliographic databases:

Document Type: Article
PACS: 11.30.Er
MSC: 15A66
Received: 18.06.2012
Revised: 02.11.2012

Citation: D. S. Shirokov, “Pauli theorem in the description of $n$-dimensional spinors in the Clifford algebra formalism”, TMF, 175:1 (2013), 11–34; Theoret. and Math. Phys., 175:1 (2013), 454–474

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. D. S. Shirokov, “Svertki po rangam i kvaternionnym tipam v algebrakh Klifforda”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 19:1 (2015), 117–135  mathnet  crossref  zmath  elib
    2. D. S. Shirokov, “On some Lie groups containing spin group in Clifford algebra”, J. Geom. Symmetry Phys., 42 (2016), 73–94  crossref  mathscinet  zmath  isi  scopus
    3. D. S. Shirokov, “Method of averaging in Clifford algebras”, Adv. Appl. Clifford Algebr., 27:1, SI (2017), 149–163  crossref  mathscinet  zmath  isi  scopus
    4. V. V. Monakhov, “Construction of a fermionic vacuum and the fermionic operators of creation and annihilation in the theory of algebraic spinors”, Phys. Part. Nuclei, 48:5 (2017), 836–838  crossref  isi  scopus
    5. D. S. Shirokov, “Clifford algebras and their applications to Lie groups and spinors”, Proceedings of the XIXth International Conference on Geometry, Integrability and Quantization, eds. I. Mladenov, A. Yoshioka, Inst. Biophysics & Biomedical Engineering Bulgarian Acad. Sciences, 2018, 11–53  crossref  mathscinet  isi
    6. Bizi N., Brouder Ch., Besnard F., “Space and Time Dimensions of Algebras With Application to Lorentzian Noncommutative Geometry and Quantum Electrodynamics”, J. Math. Phys., 59:6 (2018), 062303  crossref  mathscinet  zmath  isi  scopus
    7. Shirokov D.S., “Classification of Lie Algebras of Specific Type in Complexified Clifford Algebras”, Linear Multilinear Algebra, 66:9 (2018), 1870–1887  crossref  mathscinet  zmath  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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