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Quadratic algebras applied to noncommutative integration of the Klein-Gordon equation: Four-dimensional quadratic algebras containing three-dimensional nilpotent lie algebras

  • Physics of Elementary Particles And Field Theory
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Abstract

The study is continued on noncommutative integration of linear partial differential equations [1] in application to the exact integration of quantum-mechanical equations in a Riemann space. That method gives solutions to the Klein-Gordon equation when the set of noncommutative symmetry operations for that equation forms a quadratic algebra consisting of one second-order operator and of first-order operators forming a Lie algebra. The paper is a continuation of [2], where a single nontrivial example is used to demonstrate noncommutative integration of the Klein-Gordon equation in a Riemann space not permitting variable separation.

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Authors and Affiliations

  1. Tomsk State University, Russia

    O. L. Varaksin, V. V. Firstov, A. V. Shapovalov & I. V. Shirokov

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

Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 89–94, March, 1995.

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Varaksin, O.L., Firstov, V.V., Shapovalov, A.V. et al. Quadratic algebras applied to noncommutative integration of the Klein-Gordon equation: Four-dimensional quadratic algebras containing three-dimensional nilpotent lie algebras. Russ Phys J 38, 299–303 (1995). https://doi.org/10.1007/BF00559478

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  • DOI: https://doi.org/10.1007/BF00559478

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