Geodesic
Geometrical structure of the base and twisting of the graded fibre bundles used in modeling gravitation and elementary particles
Teoretičeskaâ i matematičeskaâ fizika, Tome 108 (1996) no. 1, pp. 16-35 
V. T. Berezin. Geometrical structure of the base and twisting of the graded fibre bundles used in modeling gravitation and elementary particles. Teoretičeskaâ i matematičeskaâ fizika, Tome 108 (1996) no. 1, pp. 16-35. http://geodesic.mathdoc.fr/item/TMF_1996_108_1_a1/
@article{TMF_1996_108_1_a1,
     author = {V. T. Berezin},
     title = {Geometrical structure of the base and twisting of the graded fibre bundles used in modeling gravitation and elementary particles},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {16--35},
     year = {1996},
     volume = {108},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1996_108_1_a1/}
}
TY  - JOUR
AU  - V. T. Berezin
TI  - Geometrical structure of the base and twisting of the graded fibre bundles used in modeling gravitation and elementary particles
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1996
SP  - 16
EP  - 35
VL  - 108
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_1996_108_1_a1/
LA  - ru
ID  - TMF_1996_108_1_a1
ER  - 
%0 Journal Article
%A V. T. Berezin
%T Geometrical structure of the base and twisting of the graded fibre bundles used in modeling gravitation and elementary particles
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1996
%P 16-35
%V 108
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_1996_108_1_a1/
%G ru
%F TMF_1996_108_1_a1

Voir la notice de l'article provenant de la source Math-Net.Ru

To deseribe the unification of the fundamental interactions of elementary particles and gravitation the graded bundle mathematical structure $\zeta$ is needed. Its base $B$ is the 9-dimensional graded space having one scalar, four spinor and four vector dimensions. One-parametric family of the Poincaré group $1P$ is found. It is shown that any group of this family acts on its invariant subgroup and on the base $B$ in different ways. This situation is different from the classical one and point out at the nontriviality of the $\zeta$-bundle geometrical properties. The problem of twisting is discussed.

[1] P. Uest, Vvedenie v supersimmetriyu i supergravitatsiyu, Mir, M., 1989 | MR

[2] Yu. Vess, Dzh. Begger, Supersimmetriya i supergravitatsiya, Mir, M., 1986 | MR

[3] M. F. Sohnius, “Introducing Supersymmetry”, Phys. Rep. (Review Section of Physics Letters), 128:2–3 (1985), 39–204, North-Holland, Amsterdam | MR

[4] D. Z. Freedman, Introduction to Supersymmetry in Particle and Nuclear Physics, Plenum Press, New York, 1984, P. 1–28 | MR

[5] M. Müller, Consistent Classical Supergravity Theories, Lecture Notes in Physics, 336, Springer-Verlag, Berlin, 1989 | MR

[6] B. de Witt, D. Z. Freedman, Supersymmetry, Plenum Press, New York, 1985, P. 135–210

[7] R. Haag, J. Lopuszanski, M. Sohnius, Nucl. Phys., B88 (1967), 257 | MR

[8] V. T. Berezin, TMF, 93:1 (1992), 154–174 | MR | Zbl

[9] K. Godbiion, Differentsialnaya geometriya i analiticheskaya mekhanika, Mir, M., 1973

[10] D. Khyuzmoller, Rassloennye prostranstva, Mir, M., 1970

[11] M. M. Postnikov, Differentsialnaya geometriya, Nauka, M., 1988 | MR | Zbl

[12] R. Zulanke, P. Vintgen, Differentsialnaya geometriya i rassloeniya, Mir, M., 1975

[13] B. de Witt, “The Spacetime Approach to Quantum Field Theory”, Relativity, groups and topology, Les Houches, Session XL. Course 5. V. II (1983), eds. B. S. de Witt and R. Stora, Elsevier Sc. Publ., 1983, 482–738 | MR

[14] F. A. Berezin, Vvedenie v algebru i analiz s antikommutiruyuschimi peremennymi, Izd-vo MGU, M., 1983 | MR

[15] G. Kein, Sovremennaya fizika elementarnykh chastits, Mir, M., 1990

[16] T.-P. Cheng, L.-F. Li, Kalibrovochnye teorii v fizike elementarnykh chastits, Mir, M., 1987

[17] L. Raider, Kvantovaya teoriya polya, Mir, M., 1987 | MR

[18] M. M. Postnikov, Gruppy i algebry Li, Nauka, M., 1982 | MR

[19] V. A. Zhelnorovich, Teoriya spinorov i ee primenenie v fizike i mekhanike, Nauka, M., 1982 | MR | Zbl