6,011 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
Locally Homogeneous Spaces, Induced Killing Vector Fields and Applications to Bianchi Prototypes
An answer to the question: Can, in general, the adoption of a given symmetry
induce a further symmetry, which might be hidden at a first level? has been
attempted in the context of differential geometry of locally homogeneous
spaces. Based on E. Cartan's theory of moving frames, a methodology for finding
all symmetries for any n dimensional locally homogeneous space is provided. The
analysis is applied to 3 dimensional spaces, whereby the embedding of them into
a 4 dimensional Lorentzian manifold is examined and special solutions to
Einstein's field equations are recovered. The analysis is mainly of local
character, since the interest is focused on local structures based on
differential equations (and their symmetries), rather than on the implications
of, e.g., the analytic continuation of their solution(s) and their dynamics in
the large.Comment: 27 pages, no figues, no tables, one reference added, spelling and
punctuation issues correcte
(1,0) superconformal theories in six dimensions and Killing spinor equations
We solve the Killing spinor equations of 6-dimensional (1,0) superconformal
theories in all cases. In particular, we derive the conditions on the fields
imposed by the Killing spinor equations and demonstrate that these depend on
the isotropy group of the Killing spinors. We focus on the models proposed by
Samtleben et al in \cite{ssw} and find that there are solutions preserving 1,2,
4 and 8 supersymmetries. We also explore the solutions which preserve 4
supersymmetries and find that many models admit string and 3-brane solitons as
expected from the M-brane intersection rules. The string solitons are smooth
regulated by the moduli of instanton configurations.Comment: 26 page
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