Geodesic
Structure of representations of the conformal supergroup in the $OSp(1,4)$ basis
Teoretičeskaâ i matematičeskaâ fizika, Tome 45 (1980) no. 1, pp. 30-45 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A new method is suggested for constructing the complete set of irreducible representations of conformal supergroup $SU(2,2/1)$ acting on superfields of the type $\Phi(k,\theta_+,\theta_-)$ ($k$ being the Lorentz index, $\theta_+$, $\theta_-$ left- and right-handed Grassmann coordinates). Its main point is the reduction of the problem to the much more simple task of extracting the minimal set of certain invariant spaces of the orthosymplectic subgroup $OSp^\mathrm{I}(1,4)$, of the supergroup $SU(2,2/1)$. These spaces are those closed also with respect to another $OSp(1,4)$-subgroup ($OSp^\mathrm{II}(1,4)$) which intersects with $OSp^\mathrm{I}(1,4)$ over $O(2,3)$ and completes it to the whole $SU(2,2/1)$. The precise criterion for selection of such invariant spaces is formulated. New series of $SU(2,2/1)$ representations are found and the problem of the equivalency between representations induced by various little (super) groups is discussed. 
@article{TMF_1980_45_1_a2,
     author = {E. A. Ivanov and A. S. Sorin},
     title = {Structure of~representations of~the conformal supergroup in~the $OSp(1,4)$ basis},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {30--45},
     year = {1980},
     volume = {45},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1980_45_1_a2/}
}
TY  - JOUR
AU  - E. A. Ivanov
AU  - A. S. Sorin
TI  - Structure of representations of the conformal supergroup in the $OSp(1,4)$ basis
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1980
SP  - 30
EP  - 45
VL  - 45
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_1980_45_1_a2/
LA  - ru
ID  - TMF_1980_45_1_a2
ER  - 
%0 Journal Article
%A E. A. Ivanov
%A A. S. Sorin
%T Structure of representations of the conformal supergroup in the $OSp(1,4)$ basis
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1980
%P 30-45
%V 45
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_1980_45_1_a2/
%G ru
%F TMF_1980_45_1_a2
E. A. Ivanov; A. S. Sorin. Structure of representations of the conformal supergroup in the $OSp(1,4)$ basis. Teoretičeskaâ i matematičeskaâ fizika, Tome 45 (1980) no. 1, pp. 30-45. http://geodesic.mathdoc.fr/item/TMF_1980_45_1_a2/

[1] J. Wess, B. Zumino, Nucl. Phys., B70 (1974), 39 | DOI | MR

[2] S. Ferrara, Nucl. Phys., B77 (1974), 73 | DOI

[3] Dao Vong Dyk, TMF, 24 (1975), 49 ; Б. Л. Анева, С. Г. Михов, Д. Ц. Стоянов, ТМФ, 35 (1978), 162

[4] V. V. Molotkov, S. G. Petrova, D. Ts. Stoyanov, TMF, 26 (1976), 188 | MR | Zbl

[5] M. Kaku, P. K. Townsend, P. van Nieuwenhuizen, Phys. Rev., D17 (1978), 317 | MR

[6] P. G. O. Freund, Ann. Phys., 84 (1974), 440 ; R. E. Kallosh, Phys. Lett., B55 (1975), 321 ; F. Englert, C. Truffin, R. Gastmans, Nucl. Phys., B117 (1976), 407 ; E. S. Fradkin, G. A. Vilkovisky, Phys. Lett., B73 (1978), 209 | DOI | DOI | DOI | DOI | MR

[7] P. H. Dondi, M. Sohnius, Nucl. Phys., B81 (1974), 317 | DOI | MR

[8] B. L. Aneva, S. G. Mikhov, D. Ts. Stoyanov, TMF, 31 (1977), 177 | MR | Zbl

[9] V. V. Molotkov, S. G. Petrova, Soobschenie OIYaI E2-10126; Сообщение ОИЯИ Р2-10127, Дубна, 1976

[10] E. Sokatchev, Nucl. Phys., B99 (1975), 96 | DOI | MR

[11] E. A. Ivanov, A. S. Sorin, Preprint JINR E2-12363, Dubna, 1979 | MR

[12] E. A. Ivanov, A. S. Sorin, Preprint JINR E2-12364, Dubna, 1979 | MR

[13] E. A. Ivanov, A. S. Sorin, TMF, 39 (1979), 172 ; препринт ОИЯИ Е2-11610, Дубна, 1978 | MR

[14] S. Coleman, J. Wess, B. Zumino, Phys. Rev., 177 (1969), 2239 ; C. G. Callan, S. Coleman, J. Wess, B. Zumino, Phys. Rev., 177 (1969), 2247 ; Д. В. Волков, ЭЧАЯ, 4 (1973), 3; V. I. Ogievetsky, Proc. X-th Winter School of Th. Phys. in Karpacz, 1, 1974, 117 | DOI | DOI | MR

[15] M. Bednář, V. Šachl, J. Math. Phys., 19 (1978), 1487 ; B. W. Keck, J. Phys., A8 (1975), 1819 | DOI | MR | Zbl | MR