Geodesic
Theory of dynamical affine and conformal symmetries as the theory of the gravitational field
Teoretičeskaâ i matematičeskaâ fizika, Tome 21 (1974) no. 3, pp. 329-342 
A. B. Borisov; V. I. Ogievetskii. Theory of dynamical affine and conformal symmetries as the theory of the gravitational field. Teoretičeskaâ i matematičeskaâ fizika, Tome 21 (1974) no. 3, pp. 329-342. http://geodesic.mathdoc.fr/item/TMF_1974_21_3_a4/
@article{TMF_1974_21_3_a4,
     author = {A. B. Borisov and V. I. Ogievetskii},
     title = {Theory of dynamical affine and conformal symmetries as the theory of the gravitational field},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {329--342},
     year = {1974},
     volume = {21},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1974_21_3_a4/}
}
TY  - JOUR
AU  - A. B. Borisov
AU  - V. I. Ogievetskii
TI  - Theory of dynamical affine and conformal symmetries as the theory of the gravitational field
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1974
SP  - 329
EP  - 342
VL  - 21
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_1974_21_3_a4/
LA  - ru
ID  - TMF_1974_21_3_a4
ER  - 
%0 Journal Article
%A A. B. Borisov
%A V. I. Ogievetskii
%T Theory of dynamical affine and conformal symmetries as the theory of the gravitational field
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1974
%P 329-342
%V 21
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_1974_21_3_a4/
%G ru
%F TMF_1974_21_3_a4

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

Invariance under the infinite-parameter generally covariant group is equivalent to simultaneous invariance under the affine and the conformal group. A nonlinear realization of the affine group (with linearization on the poincar6 group) leads to a symmetric tensor field as Goldstone field. The requirement that the theory correspond simultaneously to a realization of the conformal group as well leads uniquely to the theory of a tensor field whose equations are Einstein's. This shows that the theory of the gravitational field is the theory of spontaneous breaking of affine and conformal symmetries in the same way as chiral dynamics is the theory of spontaneous breaking of chiral symmetry. This analogy brings out new aspects of the role of gravitation in the theory of elementary particles.

[1] S. Weinberg, 1970 Brandeis Lectures, Cambridge, 1970

[2] S. Coleman, J. Wess, B. Zumino, Phys. Rev., 177 (1969), 2239 | DOI

[3] V. I. Ogievetsky, Lett. Nuovo Cim., 8 (1973), 988 | DOI | MR

[4] A. Salam, J. Strathdee, Phys. Rev., 184 (1969), 1750 | DOI | MR

[5] C. Isham, A. Salam, J. Strathdee, Ann. Phys. (N. Y.), 62 (1971), 3 | DOI | MR

[6] D. V. Volkov, EChAYa, 4 (1973), 3 ; Д. В. Волков, В. П. Акулов, Письма ЖЭТФ, 16 (1972), 621 | MR

[7] V. Ogievetsky, X Winter School of Theor. Phys. (Karpach, Poland), 1973

[8] V. I. Ogievetskii, I. V. Polubarinov, ZhETF, 48 (1965), 1625 | MR

[9] E. Kartan, Geometriya grupp Li i simmetricheskie prostranstva, Sbornik statei, IL, 1949

[10] L. D. Landau, E. M. Lifshits, Teoriya polya, «Nauka», 1967 | MR | Zbl

[11] A. Trautman, Reports of Math. Phys., 1970, no. 1, 29 | DOI | MR | Zbl

[12] C. Isham, A. Salam, Lett. Nuovo Cim., 5 (1972), 969 | DOI | MR

[13] S. Weinberg, Phys. Rev., 177 (1969), 2064 ; V. Ogievetsky, Phys. Lett., 33B (1970), 227 ; Проблемы современной физики, Сборник статей памяти И. Е. Тамма, «Наука», 1972, 224 | DOI | DOI | MR

[14] M. Gell-Mann, Phys. Rev. Lett., 14 (1965), 77 | DOI | MR

[15] L. Biedenharn, R. Cusson, M. Han, O. Weaver, Phys. Lett., 42B (1972), 257 | DOI

[16] G't. Hooft, M. Veltman, Preprint TH-1723, CERN, 1973