138 research outputs found
From Poincare to affine invariance: How does the Dirac equation generalize?
A generalization of the Dirac equation to the case of affine symmetry, with
SL(4,R) replacing SO(1,3), is considered. A detailed analysis of a Dirac-type
Poincare-covariant equation for any spin j is carried out, and the related
general interlocking scheme fulfilling all physical requirements is
established. Embedding of the corresponding Lorentz fields into
infinite-component SL(4,R) fermionic fields, the constraints on the SL(4,R)
vector-operator generalizing Dirac's gamma matrices, as well as the minimal
coupling to (Metric-)Affine gravity are studied. Finally, a symmetry breaking
scenario for SA(4,R) is presented which preserves the Poincare symmetry.Comment: 34 pages, LaTeX2e, 8 figures, revised introduction, typos correcte
World Spinors - Construction and Some Applications
The existence of a topological double-covering for the and
diffeomorphism groups is reviewed. These groups do not have finite-dimensional
faithful representations. An explicit construction and the classification of
all , unitary irreducible representations is presented.
Infinite-component spinorial and tensorial fields,
"manifields", are introduced. Particle content of the ladder manifields, as
given by the "little" group is determined. The manifields are
lifted to the corresponding world spinorial and tensorial manifields by making
use of generalized infinite-component frame fields. World manifields transform
w.r.t. corresponding representations, that are constructed
explicitly.Comment: 19 pages, Te
Spatial Geometry of the Electric Field Representation of Non-Abelian Gauge Theories
A unitary transformation \Ps [E]=\exp (i\O [E]/g) F[E] is used to simplify
the Gauss law constraint of non-abelian gauge theories in the electric field
representation. This leads to an unexpected geometrization because
\o^a_i\equiv -\d\O [E]/\d E^{ai} transforms as a (composite) connection. The
geometric information in \o^a_i is transferred to a gauge invariant spatial
connection \G^i_{jk} and torsion by a suitable choice of basis vectors for
the adjoint representation which are constructed from the electric field
. A metric is also constructed from . For gauge group ,
the spatial geometry is the standard Riemannian geometry of a 3-manifold, and
for it is a metric preserving geometry with both conventional and
unconventional torsion. The transformed Hamiltonian is local. For a broad class
of physical states, it can be expressed entirely in terms of spatial geometric,
gauge invariant variables.Comment: 16pp., REVTeX, CERN-TH.7238/94 (Some revision on Secs.3 and 5; one
reference added
Test Matter in a Spacetime with Nonmetricity
Examples in which spacetime might become non-Riemannian appear above Planck
energies in string theory or, in the very early universe, in the inflationary
model. The simplest such geometry is metric-affine geometry, in which {\it
nonmetricity} appears as a field strength, side by side with curvature and
torsion. In matter, the shear and dilation currents couple to nonmetricity, and
they are its sources. After reviewing the equations of motion and the Noether
identities, we study two recent vacuum solutions of the metric-affine gauge
theory of gravity. We then use the values of the nonmetricity in these
solutions to study the motion of the appropriate test-matter. As a
Regge-trajectory like hadronic excitation band, the test matter is endowed with
shear degrees of freedom and described by a world spinor.Comment: 14 pages, file in late
Cosmological Surrealism: More than ``Eternal Reality" is Needed
Inflationary Cosmology makes the universe ``eternal" and provides for
recurrent universe creation, ad infinitum -- making it also plausible to assume
that ``our" Big Bang was also preceeded by others, etc.. However, GR tells us
that in the ``parent" universe's reference frame, the newborn universe's
expansion will never start. Our picture of ``reality" in spacetime has to be
enlarged.Comment: 7 pages, TAUP N23
Pleba\'nski-Demia\'nski-like solutions in metric-affine gravity
We consider a (non--Riemannian) metric--affine gravity theory, in particular
its nonmetricity--torsion sector ``isomorphic'' to the Einstein--Maxwell
theory. We map certain Einstein--Maxwell electrovacuum solutions to it, namely
the Pleba\'nski--Demia\'nski class of Petrov type D metrics.Comment: 12 pages of a LaTeX-fil
The Universe out of an Elementary Particle?
We consider a model of an elementary particle as a 2 + 1 dimensional brane
evolving in a 3 + 1 dimensional space. Introducing gauge fields that live in
the brane as well as normal surface tension can lead to a stable "elementary
particle" configuration. Considering the possibility of non vanishing vacuum
energy inside the bubble leads, when gravitational effects are considered, to
the possibility of a quantum decay of such "elementary particle" into an
infinite universe. Some remarkable features of the quantum mechanics of this
process are discussed, in particular the relation between possible boundary
conditions and the question of instability towards Universe formation is
analyzed
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