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.

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

Forst on Reciprocity of Reasons: a Critique

According to Rainer Forst, (i) moral and political claims must meet a requirement of reciprocal and general acceptability (RGA) while (ii) we are under a duty in engaged discursive practice to justify such claims to others, or be able to do so, on grounds that meet RGA. The paper critically engages this view. I argue that Forst builds a key component of RGA, i.e., reciprocity of reasons, on an idea of the reasonable that undermines both (i) and (ii): if RGA builds on this idea, RGA is viciously regressive and a duty of justification to meet RGA fails to be agent transparent. This negative result opens the door for alternative conceptions of reciprocity and generality. I then suggest that a more promising conception of reciprocity and generality needs to build on an idea of the reasonable that helps to reconcile the emancipatory or protective aspirations of reciprocal and general justification with its egalitarian commitments. But this requires to downgrade RGA in the order of justification and to determine on prior, substantive grounds what level of discursive influence in reciprocal and general justification relevant agents ought to have

Some Remarks on Realization of Simplicial Algebras in Cat

In this paper we discuss why the passage from simplicial algebras over a Cat operad to algebras over that operad involves apparently unavoidable technicalities.Comment: 16 page

Deep Perceptual Mapping for Thermal to Visible Face Recognition

Cross modal face matching between the thermal and visible spectrum is a much de- sired capability for night-time surveillance and security applications. Due to a very large modality gap, thermal-to-visible face recognition is one of the most challenging face matching problem. In this paper, we present an approach to bridge this modality gap by a significant margin. Our approach captures the highly non-linear relationship be- tween the two modalities by using a deep neural network. Our model attempts to learn a non-linear mapping from visible to thermal spectrum while preserving the identity in- formation. We show substantive performance improvement on a difficult thermal-visible face dataset. The presented approach improves the state-of-the-art by more than 10% in terms of Rank-1 identification and bridge the drop in performance due to the modality gap by more than 40%.Comment: BMVC 2015 (oral

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