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Classification of F algebras and noncommutative integration of the Klein-Gordon equation in Riemannian spaces

  • Elementary Particle Physics And Field Theory
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Russian Physics Journal Aims and scope

Abstract

The method of noncommutative integration of linear differential equations [A. V. Shapovalov and I. V. Shirokov, Izv. Vyssh. Uchebn. Zaved. Fiz., No. 4, 116; No. 5, 100 (1991)] is used to integrate the Klein-Gordon equation in Riemannian spaces. The situation is investigated where the set of noncommuting symmetry operators of the Klein-Gordon equation consists of first-order operators and one second-order operator and forms a so-called F algebra, which generalizes the concept of a Lie algebra. The F algebra is a quadratic algebra in the given situation. A classification of four- and five-dimensional F algebras is given. The integration of the Klein-Gordon equation in a Riemannian space, which does not admit separation of variables, is demonstrated in a nontrivial example.

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Literature cited

  1. A. V. Shapovalov and I. V. Shirokov, Izv. Vyssh. Uchebn. Zaved., Fiz., No. 7, 92–98 (1992).

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  3. A. V. Shapovalov and I. V. Shirokov, Izv. Vyssh. Uchebn. Zaved., Fiz., No. 4, 116–122 (1991).

  4. A. V. Shapovalov and I. V. Shirokov, Izv. Vyssh. Uchebn. Zaved., Fiz., No. 5, 95–100 (1991).

  5. V. G. Fedoseev, A. V. Shapovalov, and I. V. Shirokov, Izv. Vyssh. Uchebn. Zaved., Fiz., No. 9, 33–38 (1991).

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Authors
  1. O. L. Varaksin
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  2. V. V. Firstov
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  3. A. V. Shapovalov
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  4. I. V. Shirokov
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Additional information

V. V. Kuibyshev State University, Tomsk. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 45–50, January, 1993.

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Varaksin, O.L., Firstov, V.V., Shapovalov, A.V. et al. Classification of F algebras and noncommutative integration of the Klein-Gordon equation in Riemannian spaces. Russ Phys J 36, 36–40 (1993). https://doi.org/10.1007/BF00559253

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  • DOI: https://doi.org/10.1007/BF00559253

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