Representations of spacetime diffeomorphisms. I. Canonical parametrized field theories

Journal Article · Tue Oct 15 04:00:00 EDT 1985 · Ann. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1016/0003-4916(85)90018-1· OSTI ID:6333525

Isham, C J; Kuchar, K V

The super-Hamiltonian and supermomentum in canonical geometrodynamics or in a parametried field theory on a given Riemannian background have Poisson brackets which obey the Dirac relations. By smearing the supermomentum with vector fields VepsilonL Diff..sigma.. on the space manifold ..sigma.., the Lie algebra L Diff ..sigma.. of the spatial diffeomorphism group Diff ..sigma.. can be mapped antihomomorphically into the Poisson bracket algebra on the phase space of the system. The explicit dependence of the Poisson brackets between two super-Hamiltonians on canonical coordinates (spatial metrics in geometrodynamics and embedding variables in parametrized theories) is usually regarded as an indication that the Dirac relations cannot be connected with a representation of the complete Lie algebra L Diff M of spacetime diffeomorphisms.

• Research Organization: The Blackett Laboratory, Imperial College, London SW7 2BZ, United Kingdom
• OSTI ID: 6333525
• Journal Information: Ann. Phys. (N.Y.); (United States), Journal Name: Ann. Phys. (N.Y.); (United States) Vol. 164:2; ISSN APNYA
• 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
FIELD THEORIES
GENERAL RELATIVITY THEORY
HAMILTONIANS
MAPPING
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
PHASE SPACE
QUANTUM OPERATORS
SPACE
SPACE-TIME
VECTOR FIELDS