147 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 $GL(n,R)$ and
diffeomorphism groups is reviewed. These groups do not have finite-dimensional
faithful representations. An explicit construction and the classification of
all $\bar{SL}(n,R)$, $n=3,4$ unitary irreducible representations is presented.
Infinite-component spinorial and tensorial $\bar{SL}(4,R)$ fields,
"manifields", are introduced. Particle content of the ladder manifields, as
given by the $\bar{SL}(3,R)$ "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 $\bar{Diff}(4,R)$ representations, that are constructed
explicitly.Comment: 19 pages, Te

### Non-Linear Affine Embedding of the Dirac Field from the Multiplicity-Free SL(4,R) Unirreps

The correspondence between the linear multiplicity-free unirreps of SL(4, R)
studied by Ne'eman and {\~{S}}ija{\~{c}}ki and the non-linear realizations of
the affine group is worked out. The results obtained clarify the inclusion of
spinorial fields in a non-linear affine gauge theory of gravitation.Comment: 13 pages, plain TeX, macros include

### 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

### $\bar{SL}(4,R)$ Embedding for a 3D World Spinor Equation

A generic-curved spacetime Dirac-like equation in 3D is constructed. It has,
owing to the $\bar{SL}(n,R)$ group deunitarizing automorphism, a physically
correct unitarity and flat spacetime particle properties. The construction is
achieved by embedding $\bar{SL}(3,R)$ vector operator $X_{\mu}$, that plays a
role of Dirac's $\gamma_{\mu}$ matrices, into $\bar{SL}(4,R)$. Decomposition of
the unitary irreducible spinorial $\bar{SL}(4,R)$ representations gives rise to
an explicit form of the infinite $X_{\mu}$ matrices

### Free Differential Algebras: Their Use in Field Theory and Dual Formulation

The gauging of free differential algebras (FDA's) produces gauge field
theories containing antisymmetric tensors. The FDA's extend the Cartan-Maurer
equations of ordinary Lie algebras by incorporating p-form potentials ($p >
1$). We study here the algebra of FDA transformations. To every p-form in the
FDA we associate an extended Lie derivative $\ell$ generating a corresponding
``gauge" transformation. The field theory based on the FDA is invariant under
these new transformations. This gives geometrical meaning to the antisymmetric
tensors. The algebra of Lie derivatives is shown to close and provides the dual
formulation of FDA's.Comment: 10 pages, latex, no figures. Talk presented at the 4-th Colloquium on
"Quantum Groups and Integrable Sysytems", Prague, June 199

### Yang-Mills gravity in biconformal space

We write a gravity theory with Yang-Mills type action using the biconformal
gauging of the conformal group. We show that the resulting biconformal
Yang-Mills gravity theories describe 4-dim, scale-invariant general relativity
in the case of slowly changing fields. In addition, we systematically extend
arbitrary 4-dim Yang-Mills theories to biconformal space, providing a new arena
for studying flat space Yang-Mills theories. By applying the biconformal
extension to a 4-dim pure Yang-Mills theory with conformal symmetry, we
establish a 1-1, onto mapping between a set of gravitational gauge theories and
4-dim, flat space gauge theories.Comment: 27 pages; paper emphasis shifted to focus on gravity; references
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### 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

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