Geodesic
Poisson algebra independent on boundary conditions in Ashtekar's formalism
Teoretičeskaâ i matematičeskaâ fizika, Tome 112 (1997) no. 1, pp. 142-160 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The algebra of spatial diffeomorfisms and gauge transformations is studied in the canonical formalism of General Relativity in Ashtekar and ADM variables. The previously proposed modification of a Poisson bracket by adding surface terms is exploited. It permits to consider all local functionals as admissible. It is shown that this algebra can be closed even before the fixing of boundary conditions due to a special choice of surface terms in the generators. The essential point is that the Poisson structure for the Ashtekar variables is not canonical on the boundary. 
@article{TMF_1997_112_1_a10,
     author = {V. O. Soloviev},
     title = {Poisson algebra independent on boundary conditions in {Ashtekar's} formalism},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {142--160},
     year = {1997},
     volume = {112},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1997_112_1_a10/}
}
TY  - JOUR
AU  - V. O. Soloviev
TI  - Poisson algebra independent on boundary conditions in Ashtekar's formalism
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1997
SP  - 142
EP  - 160
VL  - 112
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_1997_112_1_a10/
LA  - ru
ID  - TMF_1997_112_1_a10
ER  - 
%0 Journal Article
%A V. O. Soloviev
%T Poisson algebra independent on boundary conditions in Ashtekar's formalism
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1997
%P 142-160
%V 112
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_1997_112_1_a10/
%G ru
%F TMF_1997_112_1_a10
V. O. Soloviev. Poisson algebra independent on boundary conditions in Ashtekar's formalism. Teoretičeskaâ i matematičeskaâ fizika, Tome 112 (1997) no. 1, pp. 142-160. http://geodesic.mathdoc.fr/item/TMF_1997_112_1_a10/

[1] T. Regge, C. Teitelboim, Ann. of Phys., 88 (1974), 286 | DOI | MR | Zbl

[2] L. A. Takhtadzhyan, L. D. Faddeev, Gamiltonov podkhod v teorii solitonov, Nauka, M., 1986 | MR | Zbl

[3] D. Lewis, J. Marsden, R. Montgomery, T. Ratiu, Physica D, 18 (1986), 391 | DOI | MR | Zbl

[4] L. D. Faddeev, L. A. Takhtajan, Lett. Math. Phys., 10 (1985), 183 | DOI | MR | Zbl

[5] V. A. Arkadev, A. K. Pogrebkov, M. K. Polivanov, DAN SSSR, 298 (1988), 324 | MR | Zbl

[6] V. O. Soloviev, J. Math. Phys., 34 (1993), 5747 | DOI | MR

[7] V. O. Soloviev, Boundary values as Hamiltonian variables. II: Graded structures, Preprint IHEP 94-145, Protvino, 1994 ; E-print q-alg/9501017 | MR

[8] V. O. Soloviev, Phys. Lett. B, 292 (1992), 30 | DOI | MR

[9] L. Smolin, J. Math. Phys., 36 (1995), 6417 | DOI | MR | Zbl

[10] R. Arnovitt, S. Dizer, K. V. Misner, “Dinamika obschei teorii otnositelnosti”, Einshteinovskii sbornik, 1967, Nauka, M., 1967

[11] K. Kuchař, J. Math Phys., 17 (1977), 777 ; 792; 801; 18, 158 | DOI | MR

[12] C. Teitelboim, Ann. Phys., 79 (1973), 542 | DOI

[13] V. O. Solovev, TMF, 65 (1985), 400 | Zbl

[14] A. Ashtekar, Phys. Rev. Lett., 57 (1986), 2244 ; Phys. Rev. D, 36 (1987), 1587 ; A. Ashtekar, P. Mazur, C. G. Torre, Phys. Rev. D, 36 (1987), 2955 | DOI | MR | DOI | MR | DOI | MR

[15] M. Henneaux, J. E. Nelson, C. Schomblond, Phys. Rev. D, 39 (1989), 434 | DOI | MR | Zbl

[16] P. Olver, Prilozheniya grupp Li k differentsialnym uravneniyam, Mir, M., 1989 | MR | Zbl

[17] I. Dorfman, Dirac Structures, Integrability of Nonlinear Evolution Equations, John Wiley and Sons, N. Y., 1993 | MR

[18] L. Dickey, Soliton Equations and Hamiltonian Systems, World Scientific, Singapore, 1991 | MR | Zbl

[19] J. D. Brown, M. Henneaux, J. Math. Phys., 27 (1986), 489 | DOI | MR

[20] T. Thiemann, Class. Quant. Grav., 12 (1995), 181 | DOI | MR

[21] V. O. Solovev, O razlichii mezhdu dopustimymi i “differentsiruemymi” gamiltonianami, Preprint IFVE OTF 96-86, Protvino, 1996