Dynamical structure of gravitational theories with GL(4,R) connections

Journal Article · Mon Jul 01 04:00:00 EDT 1985 · J. Math. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1063/1.526883· OSTI ID:5545927

Antonowicz, M; Szczyrba, W

We investigate here GL (4,R)-gauge theories of gravity based on variational principles. The components of tetrad fields e/sup()/sup ..cap alpha..//sub ..mu../, the components of metrics g/sub()() alphabeta/, and the components of connections GAMMA/sub lambda//sup()/sup ..cap alpha..//sub()/sub ..beta../ are taken as the gravitational potentials. Matter potentials are the components of GL (4,R)-tensor fields phi/sup ..sigma../. We derive the conservation laws for a general theory, that is, the Belinfante--Rosenfeld and Bianchi identities, and find minimal systems of independent variational equations. The natural GL (4,R)-covariant Hamiltonian formulation of the theory induces a GL (3,R)-covariant Hamiltonian formulation related to a chosen slicing of space-time. The Hamiltonian field equations corresponding to this formulation describe the dynamics of the system. We determine 20 symplectic constraints, 20 gauge transformations, and 20 gauge variables generic for a general gravitational Lagrangian. As an example, we consider the Gl (4,R)--Einstein theory in vacuum as well as in the presence of a vector field and find the complete canonical formulation in both cases.

• Research Organization: Institute of Theoretical Physics, Warsaw University, Hoza 69, 00-681 Warsaw, Poland
• OSTI ID: 5545927
• Journal Information: J. Math. Phys. (N.Y.); (United States), Journal Name: J. Math. Phys. (N.Y.); (United States) Vol. 26:7; ISSN JMAPA
• Country of Publication: United States
• Language: English

Related Subjects

657003* -- Theoretical & Mathematical Physics-- Relativity & Gravitation
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CONSERVATION LAWS
DYNAMICS
EQUATIONS
FIELD EQUATIONS
FIELD THEORIES
FUNCTIONS
GAUGE INVARIANCE
GENERAL RELATIVITY THEORY
GEOMETRY
GRAVITATION
GROUP THEORY
HAMILTONIAN FUNCTION
INVARIANCE PRINCIPLES
LAGRANGIAN FUNCTION
LIE GROUPS
MATHEMATICS
MECHANICS
SPACE-TIME
SYMMETRY GROUPS
VECTOR FIELDS