A Superconnection for Riemannian Gravity as Spontaneously Broken SL(4,R) Gauge Theory

A superconnection is a supermatrix whose even part contains the gauge-potential one-forms of a local gauge group, while the odd parts contain the (0-form) Higgs fields; the combined grading is thus odd everywhere. We demonstrate that the simple supergroup ${\bar P}(4,R)$ (rank=3) in Kac' classification (even subgroup $\bar {SL}(4,R)$) prverline {SL}(4,R)$) provides for the most economical spontaneous breaking of$\bar{SL}(4,R)$as gauge group, leaving just local$\bar{SO}(1,3)$ unbroken. As a result, post-Riemannian SKY gravity yields Einstein's theory as a low-energy (longer range) effective theory. The theory is renormalizable and may be unitary.Comment: 11 pages, late

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

Hyperfluid - a model of classical matter with hypermomentum

A variational theory of a continuous medium is developed the elements of which carry momentum and hypermomentum (hyperfluid). It is shown that the structure of the sources in metric-affine gravity is predetermined by the conservation identities and, when using the Weyssenhoff ansatz, these explicitly yield the hyperfluid currents.Comment: plain Tex, 11 pages, no figure

The Lagrangian of q-Poincare' Gravity

The gauging of the q-Poincar\'e algebra of ref. hep-th 9312179 yields a non-commutative generalization of the Einstein-Cartan lagrangian. We prove its invariance under local q-Lorentz rotations and, up to a total derivative, under q-diffeomorphisms. The variations of the fields are given by their q-Lie derivative, in analogy with the q=1 case. The algebra of q-Lie derivatives is shown to close with field dependent structure functions. The equations of motion are found, generalizing the Einstein equations and the zero-torsion condition.Comment: 12 pp., LaTeX, DFTT-01/94 (extra blank lines introduced by mailer, corrupting LaTeX syntax, have been hopefully eliminated

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

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

Improved Energy-Momentum Currents in Metric-Affine Spacetime

In Minkowski spacetime it is well-known that the canonical energy-momentum current is involved in the construction of the globally conserved currents of energy-momentum and total angular momentum. For the construction of conserved currents corresponding to (approximate) scale and proper conformal symmetries, however, an improved energy-momentum current is needed. By extending the Minkowskian framework to a genuine metric-affine spacetime, we find that the affine Noether identities and the conformal Killing equations enforce this improvement in a rather natural way. So far, no gravitational dynamics is involved in our construction. The resulting dilation and proper conformal currents are conserved provided the trace of the energy-momentum current satisfies a (mild) scaling relation or even vanishes.Comment: 14p

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 $E^{ai}$. A metric is also constructed from $E^{ai}$. For gauge group $SU(2)$, the spatial geometry is the standard Riemannian geometry of a 3-manifold, and for $SU(3)$ 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