Equivalences of Smooth and Continuous Principal Bundles with Infinite-Dimensional Structure Group

Let K be a a Lie group, modeled on a locally convex space, and M a finite-dimensional paracompact manifold with corners. We show that each continuous principal K-bundle over M is continuously equivalent to a smooth one and that two smooth principal K-bundles over M which are continuously equivalent are also smoothly equivalent. In the concluding section, we relate our results to neighboring topics.Comment: 18 pages, final versio

Robust a priori and a posteriori error analysis for the approximation of Allen–Cahn and Ginzburg–Landau equations past topological changes

A priori and a posteriori error estimates are derived for the numerical approximation of scalar and complex valued phase field models. Particular attention is devoted to the dependence of the estimates on a small parameter and to the validity of the estimates in the presence of topological changes in the solution that represents singular points in the evolution. For typical singularities the estimates depend on the inverse of the parameter in a polynomial as opposed to exponential dependence of estimates resulting from a straightforward error analysis. The estimates naturally lead to adaptive mesh refinement and coarsening algorithms. Numerical experiments illustrate the reliability and efficiency of this approach for the evolution of interfaces and vortices that undergo topological changes

b→sℓ+ℓ−b\to s\ell^+\ell^- Transitions in Two-Higgs-Doublet Models

In this article we study $b\to s\mu^+\mu^-$ transitions and possible correlations with the anomalous magnetic moment of the muon ($a_\mu$) within two-Higgs-doublet models with generic Yukawa couplings, including the possibility of right-handed neutrinos. We perform the matching on the relevant effective Hamiltonian and calculate the leading one-loop effects for $b\to s\ell\ell^{(\prime)}$, $b\to s\gamma$, $\Delta B=\Delta S=2$, $b\to s\nu\bar\nu$ and $\ell\to\ell^\prime\gamma$ transitions in a general $R_\xi$ gauge. Concerning the phenomenology, we find that an explanation of the hints for new physics in $b\to s\mu^+\mu^-$ data is possible once right-handed neutrinos are included. If lepton flavour violating couplings are allowed, one can account for the discrepancy in $a_\mu$ as well. However, only a small portion of parameter space gives a good fit to $b\to s\mu^+\mu^-$ data and the current bound on $h\to\tau\mu$ requires the mixing between the neutral Higgses to be very small if one aims at an explanation of $a_\mu$.Comment: 40 pages, 1 table, 10 figure

Price adjustment to news with uncertain precision

Bayesian learning provides the core concept of processing noisy information. In standard Bayesian frameworks, assessing the price impact of information requires perfect knowledge of news’ precision. In practice, however, precision is rarely dis- closed. Therefore, we extend standard Bayesian learning, suggesting traders infer news’ precision from magnitudes of surprises and from external sources. We show that interactions of the different precision signals may result in highly nonlinear price responses. Empirical tests based on intra-day T-bond futures price reactions to employment releases confirm the model’s predictions and show that the effects are statistically and economically significant

Temperature Independent Renormalization of Finite Temperature Field Theory

We analyse 4-dimensional massive \vp^4 theory at finite temperature T in the imaginary-time formalism. We present a rigorous proof that this quantum field theory is renormalizable, to all orders of the loop expansion. Our main point is to show that the counterterms can be chosen temperature independent, so that the temperature flow of the relevant parameters as a function of $T$ can be followed. Our result confirms the experience from explicit calculations to the leading orders. The proof is based on flow equations, i.e. on the (perturbative) Wilson renormalization group. In fact we will show that the difference between the theories at T>0 and at T=0 contains no relevant terms. Contrary to BPHZ type formalisms our approach permits to lay hand on renormalization conditions and counterterms at the same time, since both appear as boundary terms of the renormalization group flow. This is crucial for the proof.Comment: 17 pages, typos and one footnote added, to appear in Ann.H.Poincar

Economic impacts of a premature nuclear phase-out in Switzerland

This paper investigates the economic impacts of two policy proposals: "Strom ohne Atom" (SOA) and "Moratorium Plus" (MOP), both of which contain a premature phase-out of nuclear power in Switzerland. While MOP restricts business-as-usual operation time of existing nuclear power plants to 40 years, which results in a cutback of 10-20 years, SOA foresees a reduction in operation time of 20-30 years and administers combined heat and power to substitute for nuclear energy. Based on simulations with an intertemporal multi-sector general equilibrium model of the Swiss economy, we quantify the price tags for risk reduction from nuclear power operation given additional constraints on back-up technologies. Costs of accelerating the phase-out of nuclear power for an average household amount to 200 CHF/a over the next 45 years under SOA and drop to 60 CHF/a in the case of MOP. If Switzerland were to assure carbon neutrality of a premature phase-out by the use of carbon taxes, adjustment costs would increase to 230 CHF under SOA and 110 CHF under MOP. --nuclear phase-out,computable general equilibrium