Hamiltonian dynamics of gauge theories of gravity

Journal Article · Sat May 15 00:00:00 EDT 1982 · Phys. Rev. D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.25.2548· OSTI ID:5494304

Szczyrba, W

We investigate the Hamiltonian structure of gauge theories of gravity based on arbitrary gravitational and matter field Lagrangians. The gauge group of the theory in question is the semisimple product of the local Lorentz group and the group of diffeomorphisms of spacetime (the local Poincare group). We derive formulas for the symplectic two-form ..cap omega.., the translational E, and the rotational J generators. The Hamilton equations expressed in terms of ..cap omega.., E, and J are equivalent to the variational Euler-Lagrange equations. The ten constraint equations of the theory are closely related both to properties of the symplectic two-form ..cap omega.. and to an action of the gauge group in the space of solutions. The dynamical generators E and J can be expressed by the left-hand sides of the constraint equations, that is, the constraints generate the dynamics by means of the Hamilton equations for the functions E and J. On the other hand, the action of the gauge group in the set of initial data determines their ''time'' evolution. We show that this evolution is in a one-to-one correspondence with that generated by the Hamilton equations.

• Research Organization: Institute for Theoretical Physics, University of Cologne, Zuelpicherstrasse 77, 5000 Cologne, Federal Republic of Germany
• OSTI ID: 5494304
• Journal Information: Phys. Rev. D; (United States), Journal Name: Phys. Rev. D; (United States) Vol. 25:10; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
657003 -- Theoretical & Mathematical Physics-- Relativity & Gravitation
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
EQUATIONS
FIELD EQUATIONS
FUNCTIONS
GAUGE INVARIANCE
GRAVITATIONAL FIELDS
HAMILTONIANS
INVARIANCE PRINCIPLES
LAGRANGIAN FUNCTION
LIE GROUPS
MATHEMATICAL OPERATORS
POINCARE GROUPS
QUANTUM OPERATORS
SPACE-TIME
SYMMETRY GROUPS
YANG-MILLS THEORY