Hamiltonian approach to gravitation theory and cosmology
Lecture course for 4th year students, Physical Department,
Moscow State University, kafedra "Quantum Theory and
High Energy Physics"
Abstract
The basics of construction and applications of the gravitation theory
Hamiltonian formalism are given.
The necessary information from the Riemannian geometry
of hypersurfaces is provided. The covariant 3+1-decomposition
of tensors and the transformation of the Hilbert-Einstein
action to the canonical form is presented. The geometrical
meaning of the constraint algebra and the problem of canonical
realization of the space-time diffeomorphism algebra are studied.
The procedure of reduction by means of gauge conditions is
considered both for closed spaces and for the asymptotically
flat space. In the latter case formulas for the generators
of the asymptotic Poincare group are derived. Applications
to quantum cosmology and its relation to the
inflationary scenario and the standard Friedman model are
discussed.