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

This article is cited in 10 scientific papers (total in 10 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

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

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

Bibliographic databases:

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

Citation in format AMSBIB
\by D.~S.~Shirokov
\paper Pauli theorem in the~description of $n$-dimensional spinors in the~Clifford algebra~formalism
\jour TMF
\yr 2013
\vol 175
\issue 1
\pages 11--34
\jour Theoret. and Math. Phys.
\yr 2013
\vol 175
\issue 1
\pages 454--474

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    Citing articles on Google Scholar: Russian citations, English citations
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    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. N. Bizi, Ch. Brouder, F. Besnard, “Space and time dimensions of algebras with application to Lorentzian noncommutative geometry and quantum electrodynamics”, J. Math. Phys., 59:6 (2018), 062303, 12 pp.  crossref  mathscinet  zmath  isi  scopus
    7. D. S. Shirokov, “Classification of Lie algebras of specific type in complexified Clifford algebras”, Linear Multilinear Algebra, 66:9 (2018), 1870–1887  crossref  mathscinet  zmath  isi  scopus
    8. S. P. Kuznetsov, V. V. Mochalov, V. P. Chuev, “On Pauli's theorem in Clifford algebras”, Russian Math. (Iz. VUZ), 63:11 (2019), 13–27  mathnet  crossref  crossref  isi
    9. Kuznetsov S.P., Mochalov V.V., Chuev V.P., “On Pauli'S Theorem in the Clifford Algebra R-1,R-3”, Adv. Appl. Clifford Algebr., 29:5 (2019), UNSP 103  crossref  mathscinet  isi
    10. Marchuk N.G., Shirokov D.S., “Local Generalization of Pauli'S Theorem”, Azerbaijan J. Math., 10:1 (2020), 38–56  mathscinet  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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