Cones and causal structures on topological and differentiable manifolds

General definitions for causal structures on manifolds of dimension d+1>2 are presented for the topological category and for any differentiable one. Locally, these are given as cone structures via local (pointwise) homeomorphic or diffeomorphic abstraction from the standard null cone variety in R^{d+1}. Weak and strong local cone (LC) structures refer to the cone itself or a manifold thickening of the cone respectively. After introducing cone (C-)causality, a causal complement with reasonable duality properties can be defined. The most common causal concepts of space-times are generalized to the present topological setting. A new notion of precausality precludes inner boundaries within future/past cones. LC-structures, C-causality, a topological causal complement, and precausality may be useful tools in conformal and background independent formulations of (algebraic) quantum field theory and quantum gravity.Comment: v3: 12 pages, latex+amssymb; compatibility conditions (2.5) and (3.2) with misprints corrected and improved argumen

Conformal Coupling and Invariance in Different Dimensions

Conformal transformations of the following kinds are compared: (1) conformal coordinate transformations, (2) conformal transformations of Lagrangian models for a D-dimensional geometry, given by a Riemannian manifold M with metric g of arbitrary signature, and (3) conformal transformations of (mini-)superspace geometry. For conformal invariance under this transformations the following applications are given respectively: (1) Natural time gauges for multidimensional geometry, (2) conformally equivalent Lagrangian models for geometry coupled to a spacially homogeneous scalar field, and (3) the conformal Laplace operator on the $n$-dimensional manifold $M of minisuperspace for multidimensional geometry and the Wheeler de Witt equation. The conformal coupling constant xi_c is critically distinguished among arbitrary couplings xi, for both, the equivalence of Lagrangian models with D-dimensional geometry and the conformal geometry on n-dimensional minisuperspace. For dimension D=3,4,6 or 10, the critical number xi_c={D-2}/{4(D-1)} is especially simple as a rational fraction.Comment: revised version (accepted by Int. J. Mod. Phys. D, ed.: A. Ashtekar, 2-Nov-94), 23 pages, LATEX, Uni Potsdam MATH-94/0

Algebraic Quantum Theory on Manifolds: A Haag-Kastler Setting for Quantum Geometry

Motivated by the invariance of current representations of quantum gravity under diffeomorphisms much more general than isometries, the Haag-Kastler setting is extended to manifolds without metric background structure. First, the causal structure on a differentiable manifold M of arbitrary dimension (d+1>2) can be defined in purely topological terms, via cones (C-causality). Then, the general structure of a net of C*-algebras on a manifold M and its causal properties required for an algebraic quantum field theory can be described as an extension of the Haag-Kastler axiomatic framework. An important application is given with quantum geometry on a spatial slice within the causally exterior region of a topological horizon H, resulting in a net of Weyl algebras for states with an infinite number of intersection points of edges and transversal (d-1)-faces within any neighbourhood of the spatial boundary S^2.Comment: 15 pages, Latex; v2: several corrections, in particular in def. 1 and in sec.

A regularizing commutant duality for a kinematically covariant partial ordered net of observables

We consider a net of *-algebras, locally around any point of observation, equipped with a natural partial order related to the isotony property. Assuming the underlying manifold of the net to be a differentiable, this net shall be kinematically covariant under general diffeomorphisms. However, the dynamical relations, induced by the physical state defining the related net of (von Neumann) observables, are in general not covariant under all diffeomorphisms, but only under the subgroup of dynamical symmetries. We introduce algebraically both, IR and UV cutoffs, and assume that these are related by a commutant duality. The latter, having strong implications on the net, allows us to identify a 1-parameter group of the dynamical symmetries with the group of outer modular automorphisms. For thermal equilibrium states, the modular dilation parameter may be used locally to define the notions of both, time and a causal structure.Comment: LaTeX, to appear in: Proc. XXI. Int. Sem. on Group Theor. Methods, Goslar (1996), eds. Doebner et a

Ks- and Lp-band polarimetry on stellar and bow-shock sources in the Galactic center

Infrared observations of the Galactic center (GC) provide a unique opportunity to study stellar and bow-shock polarization effects in a dusty environment. The goals of this work are to present new Ks- and Lp-band polarimetry on an unprecedented number of sources in the central parsec of the GC, thereby expanding our previous results in the H- and Ks-bands. We use AO-assisted Ks- and Lp-band observations, obtained at the ESO VLT. High precision photometry and the new polarimetric calibration method for NACO allow us to map the polarization in a region of 8" x 25" (Ks) resp. 26" x 28" (Lp). These are the first polarimetric observations of the GC in the Lp-band in 30 years, with vastly improved spatial resolution compared to previous results. This allows resolved polarimetry on bright bow-shock sources in this area for the first time at this wavelength. We find foreground polarization to be largely parallel to the Galactic plane (Ks-band: 6.1% at 20 degrees, Lp-band: 4.5% at 20 degrees, in good agreement with our previous findings and with older results. The previously described Lp-band excess in the foregound polarization towards the GC could be confirmed here for a much larger number of sources. The bow-shock sources contained in the FOV seem to show a different relation between the polarization in the observed wavelength bands than what was determined for the foreground. This points to the different relevant polarization mechanisms. The resolved polarization patterns of IRS 5 and 10W match the findings we presented earlier for IRS~1W. Additionally, intrinsic Lp-band polarization was measured for IRS 1W and 21, as well as for other, less prominent MIR-excess sources (IRS 2S, 2L, 5NE). The new data offer support for the presumed bow-shock nature of several of these sources (1W, 5, 5NE, 10W, 21) and for the model of bow-shock polarization presented in our last work.Comment: 19 pages, 18 figure