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

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

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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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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
2. W. I. Fushchych, “Additional invariance of relativistic equations of motion”, Theoret. and Math. Phys., 7:1 (1971), 323–433
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
4. S. P. Onufriichuk, “Infinite-component systems of Dirac-type equations”, Theoret. and Math. Phys., 84:3 (1990), 899–910
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