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Algebra of Implicitly Defined Constraints for Gravity as the General Form of Embedding Theory. / Paston, S. A.; Semenova, E. N.; Franke, V. A.; Sheykin, A. A.
в: Gravitation and Cosmology, Том 23, № 1, 07.03.2017, стр. 1-7.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - Algebra of Implicitly Defined Constraints for Gravity as the General Form of Embedding Theory
AU - Paston, S. A.
AU - Semenova, E. N.
AU - Franke, V. A.
AU - Sheykin, A. A.
PY - 2017/3/7
Y1 - 2017/3/7
N2 - We consider the embedding theory, the approach to gravity proposed by Regge and Teitelboim, in which 4D space-time is treated as a surface in high-dimensional flat ambient space. In its general form, which does not contain artificially imposed constraints, this theory can be viewed as an extension of GR. In the present paper we study the canonical description of the embedding theory in this general form. In this case, one of the natural constraints cannot be written explicitly,in contrast to the case where additional Einsteinian constraints are imposed. Nevertheless, it is possible to calculate all Poisson brackets with this constraint. We prove that the algebra of four emerging constraints is closed, i.e., all of them are first-class constraints. The explicit form of this algebra is also obtained.
AB - We consider the embedding theory, the approach to gravity proposed by Regge and Teitelboim, in which 4D space-time is treated as a surface in high-dimensional flat ambient space. In its general form, which does not contain artificially imposed constraints, this theory can be viewed as an extension of GR. In the present paper we study the canonical description of the embedding theory in this general form. In this case, one of the natural constraints cannot be written explicitly,in contrast to the case where additional Einsteinian constraints are imposed. Nevertheless, it is possible to calculate all Poisson brackets with this constraint. We prove that the algebra of four emerging constraints is closed, i.e., all of them are first-class constraints. The explicit form of this algebra is also obtained.
KW - canonical formalism
KW - constraint algebra
KW - Regge-Teitelboim approach
KW - isometric embedding
KW - theory of gravity
U2 - 10.1134/S0202289317010145
DO - 10.1134/S0202289317010145
M3 - Article
VL - 23
SP - 1
EP - 7
JO - Gravitation and Cosmology
JF - Gravitation and Cosmology
SN - 0202-2893
IS - 1
ER -
ID: 7733910