A Minimization Method for Relativistic Electrons in a Mean-Field Approximation of Quantum Electrodynamics

We study a mean-field relativistic model which is able to describe both the behavior of finitely many spin-1/2 particles like electrons and of the Dirac sea which is self-consistently polarized in the presence of the real particles. The model is derived from the QED Hamiltonian in Coulomb gauge neglecting the photon field. All our results are non-perturbative and mathematically rigorous.Comment: 18 pages, 3 figure

Self-consistent solution for the polarized vacuum in a no-photon QED model

We study the Bogoliubov-Dirac-Fock model introduced by Chaix and Iracane ({\it J. Phys. B.}, 22, 3791--3814, 1989) which is a mean-field theory deduced from no-photon QED. The associated functional is bounded from below. In the presence of an external field, a minimizer, if it exists, is interpreted as the polarized vacuum and it solves a self-consistent equation. In a recent paper math-ph/0403005, we proved the convergence of the iterative fixed-point scheme naturally associated with this equation to a global minimizer of the BDF functional, under some restrictive conditions on the external potential, the ultraviolet cut-off $\Lambda$ and the bare fine structure constant $\alpha$. In the present work, we improve this result by showing the existence of the minimizer by a variational method, for any cut-off $\Lambda$ and without any constraint on the external field. We also study the behaviour of the minimizer as $\Lambda$ goes to infinity and show that the theory is "nullified" in that limit, as predicted first by Landau: the vacuum totally kills the external potential. Therefore the limit case of an infinite cut-off makes no sense both from a physical and mathematical point of view. Finally, we perform a charge and density renormalization scheme applying simultaneously to all orders of the fine structure constant $\alpha$, on a simplified model where the exchange term is neglected.Comment: Final version, to appear in J. Phys. A: Math. Ge

Population genetics and reproductive strategies of african trypanosomes : revisiting available published data

Trypanosomatidae are a dangerous family of Euglenobionta parasites that threaten the health and economy of millions of people around the world. More precisely describing the population biology and reproductive mode of such pests is not only a matter of pure science, but can also be useful for understanding parasite adaptation, as well as how parasitism, specialization (parasite specificity), and complex life cycles evolve over time. Studying this parasite’s reproductive strategies and population structure can also contribute key information to the understanding of the epidemiology of associated diseases; it can also provide clues for elaborating control programs and predicting the probability of success for control campaigns (such as vaccines and drug therapies), along with emergence or re-emergence risks. Population genetics tools, if appropriately used, can provide precise and useful information in these investigations. In this paper, we revisit recent data collected during population genetics surveys of different Trypanosoma species in sub-Saharan Africa. Reproductive modes and population structure depend not only on the taxon but also on the geographical location and data quality (absence or presence of DNA amplification failures). We conclude on issues regarding future directions of research, in particular vis-à-vis genotyping and sampling strategies, which are still relevant yet, too often, neglected issues

Ground State and Charge Renormalization in a Nonlinear Model of Relativistic Atoms

We study the reduced Bogoliubov-Dirac-Fock (BDF) energy which allows to describe relativistic electrons interacting with the Dirac sea, in an external electrostatic potential. The model can be seen as a mean-field approximation of Quantum Electrodynamics (QED) where photons and the so-called exchange term are neglected. A state of the system is described by its one-body density matrix, an infinite rank self-adjoint operator which is a compact perturbation of the negative spectral projector of the free Dirac operator (the Dirac sea). We study the minimization of the reduced BDF energy under a charge constraint. We prove the existence of minimizers for a large range of values of the charge, and any positive value of the coupling constant $\alpha$. Our result covers neutral and positively charged molecules, provided that the positive charge is not large enough to create electron-positron pairs. We also prove that the density of any minimizer is an $L^1$ function and compute the effective charge of the system, recovering the usual renormalization of charge: the physical coupling constant is related to $\alpha$ by the formula $\alpha_{\rm phys}\simeq \alpha(1+2\alpha/(3\pi)\log\Lambda)^{-1}$, where $\Lambda$ is the ultraviolet cut-off. We eventually prove an estimate on the highest number of electrons which can be bound by a nucleus of charge $Z$. In the nonrelativistic limit, we obtain that this number is $\leq 2Z$, recovering a result of Lieb. This work is based on a series of papers by Hainzl, Lewin, Sere and Solovej on the mean-field approximation of no-photon QED.Comment: 37 pages, 1 figur

The relationship between students' views of the nature of science and their views of the nature of scientific measurement

The present study explores the relationship between students’ views on the nature of science (NOS) and their views of the nature of scientific measurement. A questionnaire with two-tier diagnostic multiple choice items on both the NOS and measurement was administered to 179 first year physics students with diverse school experiences. Students’ views on the NOS were classified into four ‘NOS profiles’ and views on measurement were classified according to either the point or set paradigms. The findings show that students with a NOS profile which is dominated by a belief that the laws of nature are to be discovered by scientists, are more likely to have a view of the nature of scientific measurement characterised by a belief in ‘true’ values. On the other hand, students who believe that scientific theories are inventions of scientists, constructed from observations which are then validated through further experimentation, are more likely to have a view of the nature of scientific measurement which is underpinned by the uncertain nature of scientific evidence. The implications for teaching scientific measurement at tertiary level are discussed

Exploiting Distance Technology to Foster Experimental Design as a Neglected Learning Objective in Labwork in Chemistry

This article deals with the design process of a remote laboratory for labwork in chemistry. In particular, it focuses on the mutual dependency of theoretical conjectures about learning in the experimental sciences and technological opportunities in creating learning environments. The design process involves a detailed analysis of the expert task and knowledge, e.g., spectrophotometry as a method for the determination of the concentration of a compound in a solution. In so doing, modifications in transposing tasks and knowledge to the learning situation can be monitored. The remote laboratory is described, as well as the specific features that alter the degree of fidelity of the learning situation in comparison to the expert one. It is conjectured that these alterations might represent actual benefits for learning