Authors:Ulrich Bunke, Thomas Nikolaus Abstract: Reviews in Mathematical Physics, Volume 27, Issue 05, June 2015. We consider topological T-duality of torus bundles equipped with [math]-gerbes. We show how a geometry on the gerbe determines a reduction of its band to the subsheaf of S1-valued functions which are constant along the torus fibers. We observe that such a reduction is exactly the additional datum needed for the construction of a T-dual pair. We illustrate the theory by working out the example of the canonical lifting gerbe on a compact Lie group which is a torus bundle over the associated flag manifold. It was a recent observation of Daenzer and van Erp [16] that for certain compact Lie groups and a particular choice of the gerbe, the T-dual torus bundle is given by the Langlands dual group. Citation: Reviews in Mathematical Physics PubDate: 2015-06-30T04:13:19Z DOI: 10.1142/S0129055X15500130

Authors:John R. Klauder Abstract: Reviews in Mathematical Physics, Volume 27, Issue 05, June 2015. A careful study of the classical/quantum connection with the aid of coherent states offers new insights into various technical problems. This analysis includes both canonical as well as closely related affine quantization procedures. The new tools are applied to several examples including: (1) A quantum formulation that is invariant under arbitrary classical canonical transformations of coordinates; (2) A toy model that for all positive energy solutions has singularities which are removed at the classical level when the correct quantum corrections are applied; (3) A fairly simple model field theory with non-trivial classical behavior that, when conventionally quantized, becomes trivial, but nevertheless finds a proper solution using the enhanced procedures; (4) A model of scalar field theories with non-trivial classical behavior that, when conventionally quantized, becomes trivial, but nevertheless finds a proper solution using the enhanced procedures; (5) A viable formulation of the kinematics of quantum gravity that respects the strict positivity of the spatial metric in both its classical and quantum versions; and (6) A proposal for a non-trivial quantization of [math] that is ripe for study by Monte Carlo computational methods. All of these examples use fairly general arguments that can be understood by a broad audience. Citation: Reviews in Mathematical Physics PubDate: 2015-06-30T04:13:15Z DOI: 10.1142/S0129055X15300022

Authors:Maurice A. de Gosson Abstract: Reviews in Mathematical Physics, Ahead of Print. In their simplest formulations, classical dynamics is the study of Hamiltonian flows and quantum mechanics of propagators. Both are linked, and emerge from the datum of a single classical concept, the Hamiltonian function. We study and emphasize the analogies between Hamiltonian flows and quantum propagators; this allows us to verify G. Mackey's observation that quantum mechanics (in its Weyl formulation) is a refinement of Hamiltonian mechanics. We discuss in detail the metaplectic representation, which very explicitly shows the close relationship between classical mechanics and quantum mechanics; the latter emerging from the first by lifting Hamiltonian flows to the double covering of the symplectic group. We also give explicit formulas for the factorization of Hamiltonian flows into simpler flows, and prove a quantum counterpart of these results. Citation: Reviews in Mathematical Physics PubDate: 2015-07-03T02:03:33Z DOI: 10.1142/S0129055X15300034

Authors:Marcelo M. Disconzi Abstract: Reviews in Mathematical Physics, Ahead of Print. We prove short-time existence for the Einstein–Euler-Entropy system for non-isentropic fluids with data in uniformly local Sobolev spaces. The cases of compact as well as non-compact Cauchy surfaces are covered. The method employed uses a Lagrangian description of the fluid flow which is based on techniques developed by Friedrich, hence providing a completely different proof of earlier results of Choquet-Bruhat and Lichnerowicz. This new proof is specially suited for applications to self-gravitating fluid bodies. Along the way, we review some basic definitions and ideas, giving thus a relatively self-contained exposition that also serves as an introduction to many aspects of the problem. Citation: Reviews in Mathematical Physics PubDate: 2015-06-24T07:53:52Z DOI: 10.1142/S0129055X15500142

Authors:Fabio Ciolli, Giuseppe Ruzzi, Ezio Vasselli Abstract: Reviews in Mathematical Physics, Ahead of Print. The present work tackles the existence of local gauge symmetries in the setting of Algebraic Quantum Field Theory (AQFT). The net of causal loops, previously introduced by the authors, is a model independent construction of a covariant net of local C*-algebras on any 4-dimensional globally hyperbolic space-time, aimed to capture structural properties of any reasonable quantum gauge theory. Representations of this net can be described by causal and covariant connection systems, and local gauge transformations arise as maps between equivalent connection systems. The present paper completes these abstract results, realizing QED as a representation of the net of causal loops in Minkowski space-time. More precisely, we map the quantum electromagnetic field Fμν, not free in general, into a representation of the net of causal loops and show that the corresponding connection system and the local gauge transformations find a counterpart in terms of Fμν. Citation: Reviews in Mathematical Physics PubDate: 2015-06-02T06:08:53Z DOI: 10.1142/S0129055X15500129