Geodesic
Covariant three-dimensional formulation of the composite quark model of mesons
Teoretičeskaâ i matematičeskaâ fizika, Tome 41 (1979) no. 2, pp. 205-219 
N. B. Skachkov; I. L. Solovtsov. Covariant three-dimensional formulation of the composite quark model of mesons. Teoretičeskaâ i matematičeskaâ fizika, Tome 41 (1979) no. 2, pp. 205-219. http://geodesic.mathdoc.fr/item/TMF_1979_41_2_a4/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The quasipotential approach is used to develop a three-dimensional covariant formalism for the description of composite systems of two relativistic particles. The mathematical formalism employs Lobachevskii geometry and an expansion with respect to the matrix elements of unitary (infinite-dimensional) representations of the Lorentz group. The use of harmonic analysis on the Lorentz group instead of an ordinary Fourier transformation makes it possible to go over from an integral equation to a finite-difference equation, this being a covariant three-dimensional generalization of the Schrödinger equation; it permits the finding of exact solutions.

[1] A. A. Logunov, A. N. Tavkhelidze, Nuovo Cim., 29 (1963), 380 | DOI | MR

[2] V. A. Matveev, R. M. Muradyan, A. N. Tavkhelidze, Preprint JINR E2-3498, Dubna, 1967; Preprint JINR P2-3900, Dubna, 1968

[3] R. N. Faustov, Ann. Phys. (N. Y.), 78 (1973), 176 | DOI

[4] V. G. Kadyshevsky, Nucl. Phys., B6 (1968), 125 | DOI

[5] V. G. Kadyshevsky, R. Mir-Kasimov, N. B. Skachkov, Nuovo Cim., 55A (1968), 233 ; ЭЧАЯ, 2 (1972), 635 | DOI

[6] M. A. Naimark, Lineinye predstavleniya gruppy Lorentsa, Fizmatgiz, 1958 ; И. М. Гельфанд, М. И. Граев, Н. Я. Виленкин, Обобщенные функции, вып. 5, Физматгиз, 1962 | MR | MR

[7] V. A. Fok, Teoriya prostranstva, vremeni i tyagoteniya, GITTL, 1955; Н. А. Черников, ЖЭТФ, 33 (1957), 541; Научные доклады высшей школы, 2 (1958), 1580; 3 (1959), 151; препринт ОИЯИ Р-2723, Дубна, 1961; Лекции на Межд. школе теоретической физики при ОИЯИ, т. 3, Дубна, 1964, 151 ; ЭЧАЯ, 4 (1973), 773; Я. А. Смородинский, Атомная энергия, 14 (1963), 110 | Zbl

[8] I. S. Shapiro, DAN SSSR, 106 (1956), 647 ; ЖЭТФ, 43 (1962), 1727 | Zbl

[9] Yu. M. Shirokov, ZhETF, 35 (1958), 1005

[10] MacFarlane, Rev. Mod. Phys., 34 (1962), 41 | DOI | MR | Zbl

[11] N. M. Atakishiev, R. M. Mir-Kasimov, Sh. M. Nagiev, TMF, 32 (1977), 34 ; В. А. Карманов, ЖЭТФ, 71 (1976), 339

[12] V. M. Vinogradov, TMF, 10 (1972), 338

[13] A. N. Kvinikhidze, D. Ts. Stoyanov, Preprint E2-5746, Dubna, 1971 | MR

[14] V. G. Kadyshevskii, R. M. Mir-Kasimov, N. B. Skachkov, YaF, 9 (1969), 219 | MR

[15] V. G. Kadyshevskii, R. M. Mir-Kasimov, M. Friman, YaF, 9 (1969), 646 | MR

[16] N. B. Skachkov, I. L. Solovtsov, EChAYa, 9 (1978), 5

[17] N. B. Skachkov, I. L. Solovtsov, YaF, 26 (1977), 695; препринт ОИЯИ Е2-9763, Дубна, 1976

[18] N. B. Skachkov, Preprint OIYaI E2-7159; Препринт ОИЯИ Е2-7333, Дубна, 1973; ТМФ, 22 (1975), 213

[19] N. B. Skachkov, Preprint OIYaI R2-12152, Dubna, 1979 | Zbl

[20] N. B. Skachkov, Preprint JINR E2-7890; Preprint JINR E2-8424, Dubna, 1974; Proc. of XVIII Intern. Conf. on High Energy Physics, vol. 1 (Tbilisi, 1976), p. AZ-11; JINR D1,2-10400, Dubna, 1977 ; Н. Б. Скачков, ТМФ, 25 (1975), 313 | Zbl