One-particle reducible contribution to the one-loop scalar propagator in a constant field

Recently, Gies and Karbstein showed that the two-loop Euler-Heisenberg Lagrangian receives a finite one-particle reducible contribution in addition to the well-known one-particle irreducible one. Here, we demonstrate that a similar contribution exists for the propagator in a constant field already at the one-loop level, and we calculate this contribution for the scalar QED case. We also present an independent derivation of the Gies-Karbstein result using the worldline formalism, treating the scalar and spinor QED cases in a unified manner.Comment: 13 pages, 4 figures. Minor corrections mad

Entropy Evolution of the Gas in Cooling Flow Clusters

We emphasise the importance of the gas entropy in studying the evolution of cluster gas evolving under the influence of radiative cooling. On this basis, we develop an analytical model for this evolution. We then show that the assumptions needed for such a model are consistent with a numerical solution of the same equations. We postulate that the passive cooling phase ends when the central gas temperature falls to very low values. It follows a phase during which an unspecified mechanism heats the cluster gas. We show that in such a scenario the small number of clusters containing gas with temperatures below about 1 keV is simply a consequence of the radiative cooling.Comment: Contribution to Proceedings of `The Riddle of Cooling Flows in Galaxies and Clusters of Galaxies', Charlottesville, VA, USA. May 31 -- June 4, 2003. Editors: Reiprich, T. H., Kempner, J. C., and Soker, N. Requires included style fil

Can the ANITA anomalous events be due to new physics?

The ANITA collaboration has observed two ultra-high-energy upgoing air shower events that cannot originate from Standard Model neutrinos that have traversed the Earth. Several beyond-the-standard-model physics scenarios have been proposed as explanations for these events. In this paper we present some general arguments making it challenging for new physics to explain the events. One exceptional class of models that could work is pointed out, in which metastable dark matter decays to a highly boosted lighter dark matter particle, that can interact in the Earth to produce the observed events.Comment: 12 pages, 5 figure

Rigorous Numerical Verification of Uniqueness and Smoothness in a Surface Growth Model

Based on numerical data and a-posteriori analysis we verify rigorously the uniqueness and smoothness of global solutions to a scalar surface growth model with striking similarities to the 3D Navier--Stokes equations, for certain initial data for which analytical approaches fail. The key point is the derivation of a scalar ODE controlling the norm of the solution, whose coefficients depend on the numerical data. Instead of solving this ODE explicitly, we explore three different numerical methods that provide rigorous upper bounds for its solutio

Improving the Convergence Properties of the Data Augmentation Algorithm with an Application to Bayesian Mixture Modeling

The reversible Markov chains that drive the data augmentation (DA) and sandwich algorithms define self-adjoint operators whose spectra encode the convergence properties of the algorithms. When the target distribution has uncountable support, as is nearly always the case in practice, it is generally quite difficult to get a handle on these spectra. We show that, if the augmentation space is finite, then (under regularity conditions) the operators defined by the DA and sandwich chains are compact, and the spectra are finite subsets of $[0,1)$. Moreover, we prove that the spectrum of the sandwich operator dominates the spectrum of the DA operator in the sense that the ordered elements of the former are all less than or equal to the corresponding elements of the latter. As a concrete example, we study a widely used DA algorithm for the exploration of posterior densities associated with Bayesian mixture models [J. Roy. Statist. Soc. Ser. B 56 (1994) 363--375]. In particular, we compare this mixture DA algorithm with an alternative algorithm proposed by Fr\"{u}hwirth-Schnatter [J. Amer. Statist. Assoc. 96 (2001) 194--209] that is based on random label switching.Comment: Published in at http://dx.doi.org/10.1214/11-STS365 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

The Principal Principle Implies the Principle of Indifference

We argue that David Lewis’s principal principle implies a version of the principle of indifference. The same is true for similar principles that need to appeal to the concept of admissibility. Such principles are thus in accord with objective Bayesianism, but in tension with subjective Bayesianism. 1 The Argument 2 Some Objections Me