Representations of the complete inhomogeneous de~Sitter group and equations in the five-dimensional approach.~I
Teoretičeskaâ i matematičeskaâ fizika, Tome 4 (1970) no. 3, pp. 360-382
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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.
@article{TMF_1970_4_3_a7,
author = {W. I. Fushchych},
title = {Representations of the complete inhomogeneous {de~Sitter} group and equations in the five-dimensional {approach.~I}},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {360--382},
publisher = {mathdoc},
volume = {4},
number = {3},
year = {1970},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1970_4_3_a7/}
}
TY - JOUR AU - W. I. Fushchych TI - Representations of the complete inhomogeneous de~Sitter group and equations in the five-dimensional approach.~I JO - Teoretičeskaâ i matematičeskaâ fizika PY - 1970 SP - 360 EP - 382 VL - 4 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_1970_4_3_a7/ LA - ru ID - TMF_1970_4_3_a7 ER -
%0 Journal Article %A W. I. Fushchych %T Representations of the complete inhomogeneous de~Sitter group and equations in the five-dimensional approach.~I %J Teoretičeskaâ i matematičeskaâ fizika %D 1970 %P 360-382 %V 4 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_1970_4_3_a7/ %G ru %F TMF_1970_4_3_a7
W. I. Fushchych. Representations of the complete inhomogeneous de~Sitter group and equations in the five-dimensional approach.~I. Teoretičeskaâ i matematičeskaâ fizika, Tome 4 (1970) no. 3, pp. 360-382. http://geodesic.mathdoc.fr/item/TMF_1970_4_3_a7/