Geometrodynamics vs. connection dynamics
- Univ. of Maryland, College Park (United States)
The purpose of this review is to describe in some detail the mathematical relationship between geometrodynamics and connection dynamics in the context of the classical theories of 2+1 and 3+1 gravity. The authors analyze the standard Einstein-Hilbert theory (in any spacetime dimension), the Palatini and Chern-Simons theories in 2+1 dimensions, and the Palatini and self-dual theories in 3+1 dimensions. Various matter fields are coupled to these theories and a pure spin-connection formulation of 3+1 gravity is briefly described. The authors derive the Euler-Lagrange equations of motion from an action principle and perform a Legendre transform to obtain a Hamiltonian formulation of each theory. Since constraints are present in all these theories, constraint functions are constructed and their Poisson bracket algebra is analyzed. The authors demonstrate, whenever possible, equivalences between the theories. 34 refs.
- OSTI ID:
- 5948103
- Journal Information:
- General Relativity and Gravitation; (United States), Vol. 25:8; ISSN 0001-7701
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
FIELD THEORIES
COMPARATIVE EVALUATIONS
GENERAL RELATIVITY THEORY
REVIEWS
GRAVITATION
DIMENSIONS
HAMILTONIANS
LAGRANGE EQUATIONS
SPACE-TIME
DIFFERENTIAL EQUATIONS
DOCUMENT TYPES
EQUATIONS
EVALUATION
MATHEMATICAL OPERATORS
PARTIAL DIFFERENTIAL EQUATIONS
QUANTUM OPERATORS
662110* - General Theory of Particles & Fields- Theory of Fields & Strings- (1992-)
661310 - Relativity & Gravitation- (1992-)