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TMF, 1970, Volume 4, Number 3, Pages 360–382 (Mi tmf4160)  

This article is cited in 4 scientific papers (total in 4 papers)

Representations of the complete inhomogeneous de Sitter group and equations in the five-dimensional approach. I

W. I. Fushchych


Abstract: A study is made of the irreducible representations of the complete inhomogeneous de Sitter group $\widetilde{\mathscr P}(1,4)$. Canonical and noncanonical equations of motion that are invariant under the group $\widetilde{\mathscr P}(1,4)$ are found. An equation is proposed which enables one to obtain a mass spectrum of particles that increases with the spin and isospin. A subsidiary result is an equation of motion for a particle with vanishing mass; this is a covariant generalization of the Weyl–Hammer–Wood equation. It is shown that the simplest $P$-, $T$-, $C$-invariant equation in the five-dimensional approach is the eight-component equation (6.7). Canonical transformations for Dirac-type equations are considered.

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English version:
Theoretical and Mathematical Physics, 1970, 4:3, 890–907

Bibliographic databases:

Received: 13.01.1970

Citation: W. I. Fushchych, “Representations of the complete inhomogeneous de Sitter group and equations in the five-dimensional approach. I”, TMF, 4:3 (1970), 360–382; Theoret. and Math. Phys., 4:3 (1970), 890–907

Citation in format AMSBIB
\Bibitem{Fus70}
\by W.~I.~Fushchych
\paper Representations of the complete inhomogeneous de~Sitter group and equations in the five-dimensional approach.~I
\jour TMF
\yr 1970
\vol 4
\issue 3
\pages 360--382
\mathnet{http://mi.mathnet.ru/tmf4160}
\zmath{https://zbmath.org/?q=an:0201.58402}
\transl
\jour Theoret. and Math. Phys.
\yr 1970
\vol 4
\issue 3
\pages 890--907
\crossref{https://doi.org/10.1007/BF01038303}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. L. P. Sokur, W. I. Fushchych, “Equations of motion invariant under the group $\mathscr{P}(1,n)$. II”, Theoret. and Math. Phys., 6:3 (1971), 251–262  mathnet  crossref  mathscinet  zmath
    2. W. I. Fushchych, “Additional invariance of relativistic equations of motion”, Theoret. and Math. Phys., 7:1 (1971), 323–433  mathnet  crossref  mathscinet
    3. A. G. Nikitin, W. I. Fushchych, I. I. Yurik, “Reduction of irreducible unitary representations of generalized Poincaré groups with respect to their subgroups”, Theoret. and Math. Phys., 26:2 (1976), 138–147  mathnet  crossref  mathscinet  zmath
    4. S. P. Onufriichuk, “Infinite-component systems of Dirac-type equations”, Theoret. and Math. Phys., 84:3 (1990), 899–910  mathnet  crossref  mathscinet  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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