Canonical Transformation Path to Gauge Theories of Gravity

In this paper, the generic part of the gauge theory of gravity is derived, based merely on the action principle and on the general principle of relativity. We apply the canonical transformation framework to formulate geometrodynamics as a gauge theory. The starting point of our paper is constituted by the general De~Donder-Weyl Hamiltonian of a system of scalar and vector fields, which is supposed to be form-invariant under (global) Lorentz transformations. Following the reasoning of gauge theories, the corresponding locally form-invariant system is worked out by means of canonical transformations. The canonical transformation approach ensures by construction that the form of the action functional is maintained. We thus encounter amended Hamiltonian systems which are form-invariant under arbitrary spacetime transformations. This amended system complies with the general principle of relativity and describes both, the dynamics of the given physical system's fields and their coupling to those quantities which describe the dynamics of the spacetime geometry. In this way, it is unambiguously determined how spin-0 and spin-1 fields couple to the dynamics of spacetime. A term that describes the dynamics of the free gauge fields must finally be added to the amended Hamiltonian, as common to all gauge theories, to allow for a dynamic spacetime geometry. The choice of this "dynamics Hamiltonian" is outside of the scope of gauge theory as presented in this paper. It accounts for the remaining indefiniteness of any gauge theory of gravity and must be chosen "by hand" on the basis of physical reasoning. The final Hamiltonian of the gauge theory of gravity is shown to be at least quadratic in the conjugate momenta of the gauge fields -- this is beyond the Einstein-Hilbert theory of General Relativity.Comment: 16 page

In-orbit Vignetting Calibrations of XMM-Newton Telescopes

We describe measurements of the mirror vignetting in the XMM-Newton Observatory made in-orbit, using observations of SNR G21.5-09 and SNR 3C58 with the EPIC imaging cameras. The instrument features that complicate these measurements are briefly described. We show the spatial and energy dependences of measured vignetting, outlining assumptions made in deriving the eventual agreement between simulation and measurement. Alternate methods to confirm these are described, including an assessment of source elongation with off-axis angle, the surface brightness distribution of the diffuse X-ray background, and the consistency of Coma cluster emission at different position angles. A synthesis of these measurements leads to a change in the XMM calibration data base, for the optical axis of two of the three telescopes, by in excess of 1 arcminute. This has a small but measureable effect on the assumed spectral responses of the cameras for on-axis targets.Comment: Accepted by Experimental Astronomy. 26 pages, 18 figure

Density of Surface States in Discrete Models

We consider a simple quantum model with a surface and prove the existence of a surface density of states. We show that the energy spectrum of the model is the union of the support of the bulk densities of states of the media forming the surface and the support of the surface density of states

The repulsion between localization centers in the Anderson model

In this note we show that, a simple combination of deep results in the theory of random Schr\"odinger operators yields a quantitative estimate of the fact that the localization centers become far apart, as corresponding energies are close together

Disentangling performance-monitoring signals encoded in feedback-related EEG dynamics

The feedback-related negativity (FRN) is a well-established electrophysiological correlate of feedback-processing. However, there is still an ongoing debate whether the FRN is driven by negative or positive reward prediction errors (RPE), valence of feedback, or mere surprise. Our study disentangles independent contributions of valence, surprise, and RPE on the feedback-related neuronal signal including the FRN and P3 components using the statistical power of a sample of N = 992 healthy individuals. The participants performed a modified time-estimation task, while EEG from 64 scalp electrodes was recorded. Our results show that valence coding is present during the FRN with larger amplitudes for negative feedback. The FRN is further modulated by surprise in a valence-dependent way being more positive-going for surprising positive outcomes. The P3 was strongly driven by both global and local surprise, with larger amplitudes for unexpected feedback and local deviants. Behavioral adaptations after feedback and FRN just show small associations. Results support the theory of the FRN as a representation of a signed RPE. Additionally, our data indicates that surprising positive feedback enhances the EEG response in the time window of the P3. These results corroborate previous findings linking the P3 to the evaluation of PEs in decision making and learning tasks

Sharpness of the phase transition and exponential decay of the subcritical cluster size for percolation on quasi-transitive graphs

We study homogeneous, independent percolation on general quasi-transitive graphs. We prove that in the disorder regime where all clusters are finite almost surely, in fact the expectation of the cluster size is finite. This extends a well-known theorem by Menshikov and Aizenman & Barsky to all quasi-transitive graphs. Moreover we deduce that in this disorder regime the cluster size distribution decays exponentially, extending a result of Aizenman & Newman. Our results apply to both edge and site percolation, as well as long range (edge) percolation. The proof is based on a modification of the Aizenman & Barsky method.Comment: Latex 2e; 25 pages (a4wide); small editorial corrections; one reference adde

Illumination in symbiotic binary stars: Non-LTE photoionization models. II. Wind case

We describe a non-LTE photoionization code to calculate the wind structure and emergent spectrum of a red giant wind illuminated by the hot component of a symbiotic binary system. We consider spherically symmetric winds with several different velocity and temperature laws and derive predicted line fluxes as a function of the red giant mass loss rate, \mdot. Our models generally match observations of the symbiotic stars EG And and AG Peg for \mdot about 10^{-8} \msunyr to 10^{-7} \msunyr. The optically thick cross- section of the red giant wind as viewed from the hot component is a crucial parameter in these models. Winds with cross-sections of 2--3 red giant radii reproduce the observed fluxes, because the wind density is then high, about 10^9 cm^{-3}. Our models favor winds with acceleration regions that either lie far from the red giant photosphere or extend for 2--3 red giant radii.Comment: 51 pages, LaTeX including three tables, requires 15 Encapsulated Postscript figures, to appear in Ap