Almost product manifolds as the low energy geometry of Dirichlet branes

Any candidate theory of quantum gravity must address the breakdown of the classical smooth manifold picture of space-time at distances comparable to the Planck length. String theory, in contrast, is formulated on conventional space-time. However, we show that in the low energy limit, the dynamics of generally curved Dirichlet p-branes possess an extended local isometry group, which can be absorbed into the brane geometry as an almost product structure. The induced kinematics encode two invariant scales, namely a minimal length and a maximal speed, without breaking general covariance. Quantum gravity effects on D-branes at low energy are then seen to manifest themselves by the kinematical effects of a maximal acceleration. Experimental and theoretical implications of such new kinematics are easily derived. We comment on consequences for brane world phenomenology.Comment: 12 pages, invited article in European Physical Journal C, reprinted in Proceedings of the International School on Subnuclear Physics 2003 Erice (World Scientific

Quantum-electrodynamical approach to the Casimir force problem

We derive the Casimir force expression from Maxwell's stress tensor by means of original quantum-electro-dynamical cavity modes. In contrast with similar calculations, our method is straightforward and does not rely on intricate mathematical extrapolation relations

How quantizable matter gravitates: a practitioner's guide

We present the practical step-by-step procedure for constructing canonical gravitational dynamics and kinematics directly from any previously specified quantizable classical matter dynamics, and then illustrate the application of this recipe by way of two completely worked case studies. Following the same procedure, any phenomenological proposal for fundamental matter dynamics must be supplemented with a suitable gravity theory providing the coefficients and kinematical interpretation of the matter equations, before any of the two theories can be meaningfully compared to experimental data.Comment: 45 pages, no figure

Geometry of physical dispersion relations

To serve as a dispersion relation, a cotangent bundle function must satisfy three simple algebraic properties. These conditions are derived from the inescapable physical requirements to have predictive matter field dynamics and an observer-independent notion of positive energy. Possible modifications of the standard relativistic dispersion relation are thereby severely restricted. For instance, the dispersion relations associated with popular deformations of Maxwell theory by Gambini-Pullin or Myers-Pospelov are not admissible.Comment: revised version, new section on applications added, 46 pages, 9 figure

All spacetimes beyond Einstein (Obergurgl Lectures)

Which geometries on a smooth manifold (apart from Lorentzian metrics) can serve as a spacetime structure? This question is comprehensively addressed from first principles in eight lectures, exploring the kinematics and gravitational dynamics of all tensorial geometries on a smooth manifold that can carry predictive matter equations, are time-orientable, and allow to distinguish positive from negative particle energies.Comment: 44 pages, 7 figures, Lectures held for the Elitestudiengang Physik Erlangen and Regensburg at Obergurgl/Austria, September 201

The Clump Mass Function of the Dense Clouds in the Carina Nebula Complex

We want to characterize the properties of the cold dust clumps in the Carina Nebula Complex (CNC), which shows a very high level of massive star feedback. We derive the Clump Mass Function (ClMF), explore the reliability of different clump extraction algorithms, and investigate the influence of the temperatures within the clouds on the resulting shape of the ClMF. We analyze a 1.25x1.25 deg^2 wide-field sub-mm map obtained with LABOCA (APEX), which provides the first spatially complete survey of the clouds in the CNC. We use the three clump-finding algorithms CLUMPFIND (CF), GAUSSCLUMPS (GC) and SExtractor (SE) to identify individual clumps and determine their total fluxes. In addition to assuming a common `typical' temperature for all clouds, we also employ an empirical relation between cloud column densities and temperature to determine an estimate of the individual clump temperatures, and use this to determine individual clump masses. While the ClMF based on the CF extraction is very well described by a power-law, the ClMFs based on GC and SE are better represented by a log-normal distribution. We also find that the use of individual clump temperatures leads to a shallower ClMF slope than the assumption of a common temperature (e.g. 20 K) of all clumps. The power-law of dN/dM \propto M^-1.95 we find for the CF sample is in good agreement with ClMF slopes found in previous studies of other regions. The dependence of the ClMF shape (power-law vs. log-normal distribution) on the employed extraction method suggests that observational determinations of the ClMF shape yields only very limited information about the true structure of the cloud. Interpretations of log-normal ClMF shape as a signature of turbulent pre-stellar clouds vs. power-law ClMFs as a signature of star-forming clouds may be taken with caution for a single extraction algorithm without additional information.Comment: 8 pages, 7 figures, accepted by A&

Brans-Dicke geometry

We reveal the non-metric geometry underlying omega-->0 Brans-Dicke theory by unifying the metric and scalar field into a single geometric structure. Taking this structure seriously as the geometry to which matter universally couples, we show that the theory is fully consistent with solar system tests. This is in striking constrast with the standard metric coupling, which grossly violates post-Newtonian experimental constraints.Comment: 8 pages, v2 with additional comment and reference