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

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.

Original language	English
Pages (from-to)	1097-1101
Number of pages	5
Journal	Soviet Physics Journal
Volume	18
Issue number	8
DOIs	https://doi.org/10.1007/BF01110028
Publication status	Published - Aug 1975

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Physics and Astronomy(all)

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10.1007/BF01110028

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title = "Completeness and orthogonality of the null plane of one class of solutions of the relativistic wave equations",

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.",

author = "Gitman, {D. M.} and Shakhmatov, {V. M.} and Shvartsman, {Sh M.}",

year = "1975",

month = aug,

doi = "10.1007/BF01110028",

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AU - Gitman, D. M.

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AU - Shvartsman, Sh M.

PY - 1975/8

Y1 - 1975/8

N2 - 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.

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

Abstract

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