Abstract
In this article, in the Clifford algebra \(R_{1,3}\), we investigated Pauli’s theorem. An algorithm for constructing Pauli’s operator is given. It is shown that the problem of constructing Pauli’s operator is related to the problem of zero divisor in Clifford algebras. Pauli’s operators for generating a basis composed of elements of of first, third or mixed rank are found.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Lounesto, P.: Clifford Algebras and Spinors, p. 346p. Cambridge University Press, Cambridge (2011)
Marchuk, N.G.: Demonstration performance and tensor products of Clifford algebra. Proc. Steklov Inst. Math. VA Steklov 290, 154–165 (2015)
Marchuk, N.G., Marchuk, N.G.: Equations of field theory and Clifford algebras, p. 304. RKhD, Moscow (2009)
Marchuk, N.G., Shirokov, D.S.: Introduction to the theory of Clifford algebras, p. 590. Moskva, Fazis (2012)
Shirokov D.S.: Method of generalized Reynolds operators and Pauli’s theorem in Clifford algebras (2016). arxiv: 1409.8163 v2 [math-ph]
Shirokov, D.S.: Extension of Pauli’s theorem to Clifford algebras. Dokl. Math. 84(2), 699–701 (2011)
Shirokov, D.S.: The generalization of the Pauli theorem to the case of Clifford algebras. Nanostruct. Math. Phys. Model. 9(1), 93–104 (2013)
Shirokov, D.S.: Pauli theorem in the description of n-dimensional spinors in the Clifford algebra formalism. Theoret. Math. Phys. 175(1), 454–474 (2013)
Shirokov, D.S.: The use of the generalized Paulis theorem for odd elements of Clifford algebra to analyze relations between spin and orthogonal groups of arbitrary dimensions. Vestn. Samar. Gos. Tekhn. Univ Ser. Fiz-Mat. Nauki 1 30, 279–287 (2013)
Shirokov, D.S.: Calculations of elements of spin groups using generalized Pauli’s theorem. Adv. Appl. Clifford Algebras 25(1), 227–244 (2015). arXiv 14, 092, 449
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by Pierre-Philippe Dechant
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Kuznetsov, S.P., Mochalov, V.V. & Chuev, V.P. On Pauli’s Theorem in the Clifford Algebra \({\varvec{R}}_\mathbf{1,3 } \). Adv. Appl. Clifford Algebras 29, 103 (2019). https://doi.org/10.1007/s00006-019-1009-5
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s00006-019-1009-5