Abstract
We study Pauli’s theorem in Clifford algebras. We offer an algorithm for constructing the Pauli operator and show that the problem of constructing the Pauli operator is connected with that of zero divisors in Clifford algebras.
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References
Lounesto, P. Clifford Algebras and Spinors (Cambridge Univ. Press, 2001).
Marchuk, N.G., Shirokov, D.S. Introduction to the theory of Clifford algebras (Fazis, Moscow, 2012) [in Russian].
Marchuk, N.G. “Demonstration representation and tensor products of Clifford algebra”, Tr. matem. inst. im. V.A. Steklova 290, 154–165 (2015).
Shirokov, D.S. “Generalization of Pauli’s theorem to the case of Clifford algebras”, Dokl. Akad. Nauk 440(5), 607–610 (2011).
Shirokov, D.S. “Generalization of Pauli’s theorem to the case of Clifford algebras”, Nanostructures. Mathematical Phisycs and Modelling 9(1), 93–104 (2013).
Shirokov, D.S. “Calculations of elements of spin groups using generalized Pauli’s theorem”, Adv. in Appl. Clifford Algebras 25(1), 227–244 (2015).
Shirokov, D.S. “Method of generalized Reynolds operators and Pauli’s theorem in Clifford algebras”, (2014), 14 pp., arXiv: 1409.8163 v2 [math-ph].
Shirokov, D.S. “Pauli’s theorem in the description of n-dimensional spinors in the Clifford algebra formalism”, TMF 175(1), 11–34 (2013).
Shirokov, D.S. “The use of the generalized Pauli’s theorem for odd elements of a Clifford algebra to analize relations between spin and orthogonal groups of arbitrary dimensions”, Vestn. Samarsk. gos. tekhn. univ. Ser. Fiz.-matem. nauki 1(30), 279–287 (2013).
Shirokov, D.S. “Method of averaging in Clifford Algebras”, Adv. in Appl. Clifford Algebras 27(1), 149–163 (2017), arXiv: 1412.0246.
Ivanitskii, A. Yu., Kuznetsov, S.P., Mochalov, V.V., Chuev, V.P. “Inverse elements and zero divisors in Clifford and Grassmann algebras”, Vestn. Chuvashsk. univ. Informatik, vychisl. tekhnika i upravlenie 3, 207–221 (2017).
Burlakov, M.P., Pokazeev, V.V., Freidenzon, L.E. Clifford analysis. 1. Clifford B-algebras (Checheno-Ingush. uviv., Groznyi, 1988), archives of VINITI, 11.03.88, no. 1959.
Kuznetsov, S.P., Mochalov, V.V. “Automorphisms of a Clifford algebra and strong regular functions”, Russian Mathematics 36(10), 81–84 (1992).
Kuznetsov, S.P., Mochalov, V.V. “Laplace operator representation and strongly regular functions in Clifford algebras” (in: Aktualn. zadachi matem. i mekhan., 56–70 (Chuvashsk. University Press, Cheboksary, 1995)).
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Russian Text © The Author(s), 2019, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2019, No. 11, pp. 16–31.
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Kuznetsov, S.P., Mochalov, V.V. & Chuev, V.P. On Pauli’s Theorem in Clifford Algebras. Russ Math. 63, 13–27 (2019). https://doi.org/10.3103/S1066369X19110033
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DOI: https://doi.org/10.3103/S1066369X19110033