Algebra of Implicitly Defined Constraints for Gravity as the General Form of Embedding Theory

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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

BibTeX

@article{d388ee5db6424bd6be264dcdd4359844,

title = "Algebra of Implicitly Defined Constraints for Gravity as the General Form of Embedding Theory",

abstract = "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.",

keywords = "canonical formalism, constraint algebra, Regge-Teitelboim approach, isometric embedding, theory of gravity",

author = "Paston, {S. A.} and Semenova, {E. N.} and Franke, {V. A.} and Sheykin, {A. A.}",

year = "2017",

month = mar,

day = "7",

doi = "10.1134/S0202289317010145",

language = "English",

volume = "23",

pages = "1--7",

journal = "Gravitation and Cosmology",

issn = "0202-2893",

publisher = "МАИК {"}Наука/Интерпериодика{"}",

number = "1",

}

RIS

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