Hamiltonian dynamics of higher-order theories of gravity

Journal Article · Wed Dec 31 23:00:00 EST 1986 · J. Math. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1063/1.527797· OSTI ID:6681814

Szczyrba, V

The Hamiltonian dynamics of gravitational theories with general Lagrangians quadratic in components of the curvature tensor is investigated. It is shown that the Noether generator corresponding to the action of the diffeomorphism group of space-time naturally defines the energy-momentum function E. The analysis of the differential of E gives rise to a formula for the symplectic two-form ..cap omega.. and thereby defines symplectic (canonical) variables of the system. This construction is four-covariant, that is, independent of a chosen slicing of space-time. A more thorough analysis is performed in the (3+1) decomposition. In this scheme the canonical classification of quadratic Lagrangians is presented. It singles out the class of canonically regular Lagrangians as well as four classes of degenerate ones. The Cauchy--Kowalewska problem for all these classes is formulated.

• Research Organization: Department of Physics, Yale University, 217 Prospect Street, New Haven, Connecticut 06511
• OSTI ID: 6681814
• Journal Information: J. Math. Phys. (N.Y.); (United States), Journal Name: J. Math. Phys. (N.Y.); (United States) Vol. 28:1; ISSN JMAPA
• Country of Publication: United States
• Language: English

Related Subjects

657003* -- Theoretical & Mathematical Physics-- Relativity & Gravitation
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ASYMPTOTIC SOLUTIONS
DIFFERENTIAL GEOMETRY
ENERGY-MOMENTUM TENSOR
FIELD THEORIES
FUNCTIONS
GENERAL RELATIVITY THEORY
GEOMETRY
GRAVITATION
HAMILTONIAN FUNCTION
LAGRANGIAN FIELD THEORY
LAGRANGIAN FUNCTION
MATHEMATICS
QUANTUM FIELD THEORY
QUANTUM GRAVITY
TENSORS