Geodesic
Infinite-component systems of Dirac-type equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 84 (1990) no. 3, pp. 323-338 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Poincaré-covariant countable systems of first-order differential equations that describe the states of a particle with fixed mass and arbitrary fixed spin and correspond to positive energy alone are obtained. The conditions of compatibility for these systems are investigated, and a group-theoretical analysis of them is made. The problem of compatibility of manifestly covariant systems of equations is solved for particles of arbitrary spin in the case when the matrix coefficients realize an arbitrary finite-dimensional representation of the algebra $AO(2,3)$. Manifestly covariant finite-dimensional equations for arbitrary spin $s$ that possess nontrivial solutions are proposed. 
@article{TMF_1990_84_3_a0,
     author = {S. P. Onufriichuk},
     title = {Infinite-component systems {of~Dirac-type} equations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {323--338},
     year = {1990},
     volume = {84},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1990_84_3_a0/}
}
TY  - JOUR
AU  - S. P. Onufriichuk
TI  - Infinite-component systems of Dirac-type equations
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1990
SP  - 323
EP  - 338
VL  - 84
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_1990_84_3_a0/
LA  - ru
ID  - TMF_1990_84_3_a0
ER  - 
%0 Journal Article
%A S. P. Onufriichuk
%T Infinite-component systems of Dirac-type equations
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1990
%P 323-338
%V 84
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_1990_84_3_a0/
%G ru
%F TMF_1990_84_3_a0
S. P. Onufriichuk. Infinite-component systems of Dirac-type equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 84 (1990) no. 3, pp. 323-338. http://geodesic.mathdoc.fr/item/TMF_1990_84_3_a0/

[1] Dirac P. A. M., Proc. Roy. Soc. Lond. A, 322 (1972), 435–445 | DOI

[2] Dirac P. A. M., Proc. Roy. Soc. Lond. A, 328 (1972), 1–7 | DOI

[3] Staunton L. P., Phys. Rev. D, 10:6 (1974), 1760–1767 | DOI | MR

[4] Biedenharn L. C., Han M. Y., van Dam H., Phys. Rev. D, 8:6 (1973), 1735–1746 | DOI | MR

[5] Browne S., Nucl. Phys., B79 (1974), 70–76 | DOI

[6] Onufriichuk S. P., Puankare-kovariantnye schetnye sistemy differentsialnykh uravnenii pervogo poryadka, Preprint 78.29, In-t matematiki AN USSR, Kiev, 1978 | MR

[7] Onufriichuk S. P., “O teoretiko-gruppovykh svoistvakh schetnykh sistem uravnenii tipa Diraka”, Simmetriya i resheniya nelineinykh uravnenii matematicheskoi fiziki, In-t matematiki AN USSR, Kiev, 1987, 108–110 | MR

[8] Fuschich V. I., TMF, 4:3 (1970), 360–382 | MR

[9] Sokur L. P., Fuschich V. I., TMF, 6:3 (1971), 348–363 | MR | Zbl

[10] Bacri M. M., J. Math. Phys., 10:2 (1969), 298–320 | DOI | MR

[11] Bacri M. M., Ghaleb A. F., Hessein M. J., J. Math. Phys., 11:7 (1970), 2015–2026 | DOI | MR

[12] Bacri M. M., J. Math. Phys., 11:7 (1970), 2027–2041 | DOI | MR

[13] Gelfand I. M., Minlos R. A., Shapiro Z. Ya., Predstavleniya gruppy vraschenii i gruppy Lorentsa, Fizmatgiz, M., 1958

[14] Jaffe L., J. Math. Phys., 12:5 (1971), 882–891 | DOI | MR