28 research outputs found
Conditional Symmetries, the True Degree of Freedom and G.C.T. Invariant Wave functions for the general Bianchi Type II Vacuum Cosmology
The quantization of the most general Bianchi Type II geometry -with all six
scale factors, as well as the lapse function and the shift vector, present- is
considered. In an earlier work, a first reduction of the initial 6-dimensional
configuration space, to a 4-dimensional one, has been achieved by the usage of
the information furnished by the quantum form of the linear constraints.
Further reduction of the space in which the wave function -obeying the
Wheeler-DeWitt equation- lives, is accomplished by unrevealling the extra
symmetries of the Hamiltonian. These symmetries appear in the form of -linear
in momenta- first integrals of motion. Most of these symmetries, correspond to
G.C.T.s through the action of the automorphism group. Thus, a G.C.T. invariant
wave function is found, which depends on the only true degree of freedom, i.e.
the unique curvature invariant, characterizing the hypersurfaces t=const.Comment: 10 pages, no figures, LaTeX2e Typesetting syste
Automorphism Inducing Diffeomorphisms, Invariant Characterization of Homogeneous 3-Spaces and Hamiltonian Dynamics of Bianchi Cosmologies
An invariant description of Bianchi Homogeneous (B.H.) 3-spaces is presented,
by considering the action of the Automorphism Group on the configuration space
of the real, symmetric, positive definite, matrices. Thus, the
gauge degrees of freedom are removed and the remaining (gauge invariant)
degrees, are the --up to 3-- curvature invariants. An apparent discrepancy
between this Kinematics and the Quantum Hamiltonian Dynamics of the lower Class
A Bianchi Types, occurs due to the existence of the Outer Automorphism
Subgroup. This discrepancy is satisfactorily removed by exploiting the quantum
version of some classical integrals of motion (conditional symmetries) which
are recognized as corresponding to the Outer Automorphisms.Comment: 18 pages, LaTeX2e, no figures, one table, to appear in Communications
in Mathematical Physic
Towards Canonical Quantum Gravity for G1 Geometries in 2+1 Dimensions with a Lambda--Term
The canonical analysis and subsequent quantization of the (2+1)-dimensional
action of pure gravity plus a cosmological constant term is considered, under
the assumption of the existence of one spacelike Killing vector field. The
proper imposition of the quantum analogues of the two linear (momentum)
constraints reduces an initial collection of state vectors, consisting of all
smooth functionals of the components (and/or their derivatives) of the spatial
metric, to particular scalar smooth functionals. The demand that the
midi-superspace metric (inferred from the kinetic part of the quadratic
(Hamiltonian) constraint) must define on the space of these states an induced
metric whose components are given in terms of the same states, which is made
possible through an appropriate re-normalization assumption, severely reduces
the possible state vectors to three unique (up to general coordinate
transformations) smooth scalar functionals. The quantum analogue of the
Hamiltonian constraint produces a Wheeler-DeWitt equation based on this reduced
manifold of states, which is completely integrated.Comment: Latex 2e source file, 25 pages, no figures, final version (accepted
in CQG