10,034 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
Dynamical symmetry enhancement near N=2, D=4 gauged supergravity horizons
We show that all smooth Killing horizons with compact horizon sections of
4-dimensional gauged N=2 supergravity coupled to any number of vector
multiplets preserve supersymmetries, where
is a pull-back of the Hodge bundle of the special K\"ahler manifold on the
horizon spatial section. We also demonstrate that all such horizons with
exhibit an SL(2,R) symmetry and preserve either 4 or 8
supersymmetries. If the orbits of the SL(2,R) symmetry are 2-dimensional, the
horizons are warped products of AdS2 with the horizon spatial section.
Otherwise, the horizon section admits an isometry which preserves all the
fields. The proof of these results is centered on the use of index theorem in
conjunction with an appropriate generalization of the Lichnerowicz theorem for
horizons that preserve at least one supersymmetry. In all
cases, we specify the local geometry of spatial horizon sections and
demonstrate that the solutions are determined by first order non-linear
ordinary differential equations on some of the fields.Comment: 60 pages, late
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
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