Representations of spacetime diffeomorphisms. I. Canonical parametrized field theories
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), Vol. 164:2
- Country of Publication:
- United States
- Language:
- English
Similar Records
Dirac constraint quantization of a parametrized field theory by anomaly-free operator representations of spacetime diffeomorphisms
Conformal geometrodynamics: True degrees of freedom in a truly canonical structure
Related Subjects
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
GENERAL RELATIVITY THEORY
SPACE-TIME
HAMILTONIANS
MAPPING
PHASE SPACE
VECTOR FIELDS
FIELD THEORIES
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
QUANTUM OPERATORS
SPACE
657003* - Theoretical & Mathematical Physics- Relativity & Gravitation
645400 - High Energy Physics- Field Theory