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Completeness and orthogonality of the null plane of one class of solutions of the relativistic wave equations

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Abstract

Possible redefinitions of the scalar product are analyzed for relativistic wave fields of the Klein-Gordon and Dirac types. It is shown that for an entire class of new exact solutions, for which it was previously not possible to define the usual scalar product on the x0=const plane, it is possible to find a correct scalar product on the null plane x0−x3=const. Orthogonality and completeness relations are proved for this scalar product. Possible applications of the results are discussed.

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Author information

Authors and Affiliations

  1. Tomsk Institute of Automated Control Systems and Radio Electronics, USSR

    D. M. Gitman, V. M. Shakhmatov & Sh. M. Shvartsman

Authors
  1. D. M. Gitman
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  2. V. M. Shakhmatov
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  3. Sh. M. Shvartsman
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Additional information

Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 43–49, August, 1975.

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Gitman, D.M., Shakhmatov, V.M. & Shvartsman, S.M. Completeness and orthogonality of the null plane of one class of solutions of the relativistic wave equations. Soviet Physics Journal 18, 1097–1101 (1975). https://doi.org/10.1007/BF01110028

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  • DOI: https://doi.org/10.1007/BF01110028

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