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geometry, gravitation and external attributes of elementary particles, whose symmetries are not
restricted only by the Lorentz group...
Difficulties arise, however, with physical
interpretation of spinorial linear representations of GLD, R), which is reduced to the infinite sums of
OC)-spinors [30, 83, 97, 78]...
Generally a family of coset representatives {a>} is defined by a certain global section
of the L-principal bundle SLD, R)^SLD, R)/L...
In our opinion, the reason lies in
the fact of the absence as yet of any observable sources, which may be identified with shear and
dilatation currents and would generate non-metricity gauge fields like a spin generating torsion...
But
the same invariance condition had motivated Utiyama's insertion of tetrad fields in his Lorentz gauge
gravitation model, and hence the gauge status of tetrad fields in this Poincare gauge model has nothing
to do with gauge potentials of the translation group...
A0.5)
One easily sees that just the component ACT is responsible for the inhomogeneous transformation law
of the connection AT under gauge translations, while 9a remains invariant under these transformations
and satisfies the linear law of gauge Lorentz transformations...
Indeed, a generalized affine connection A on the affine frame bundle AX defines a linear connection
D...
Metric and connection represent two independent geometric objects of space-time geometry, but in
gravitation theory this independence is not absolute because EP, postulating parallel translations
preserving Lorentz invariants, establishes the metricity constraint
on the pseudo-Riemannian metric g and the Lorentz connection /", whose variations can, therefore, not
be independent...
Pronin) quite like the well-known case of the Einstein gravity field (in the last case such terms can
lead to non-singular de-Sitter type inflationary cosmology (Guth, Starobinski, Gurovich)...
Thus to classify the manifolds, admitting a
gravitation structure, we have only the single topological characteristic - the Pontrjagin class pu but the
zero value Euler class of T(X4) represents the necessary and sufficient condition for a gravitational field
D...
Many four-dimensional manifolds admitting metrics
with self-dual Riemannian curvatures have been discovered and, in particular, their Euler and
Pontrjagin numbers have been computed (for a review, see [24])...
Such topological models are
produced by different gluing of real projective spaces RP' corresponding to prespinors themselves...
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