Three-loop Euler-Heisenberg Lagrangian and asymptotic analysis in 1+1 QED

In recent years, the Euler-Heisenberg Lagrangian has been shown to be a useful tool for the analysis of the asymptotic growth of the N-photon amplitudes at large N. Moreover, certain results and conjectures on its imaginary part allow one, using Borel analysis, to make predictions for those amplitudes at large loop orders. Extending work by G.V. Dunne and one of the authors to the three-loop level, but in the simpler context of 1+1 dimensional QED, we calculate the corresponding Euler-Heisenberg Lagrangian, analyse its weak field expansion, and study the congruence with predictions obtained from worldline instantons. We discuss the relevance of these issues for Cvitanovic's conjecture.Comment: 8 pages, 1 figure, Talk given by C. Schubert at QFEXT09, Univ. of Oklahoma, Norman, September 21 - 25, 2009, to appear in the conference proceeding

Integral representations combining ladders and crossed-ladders

We use the worldline formalism to derive integral representations for three classes of amplitudes in scalar field theory: (i) the scalar propagator exchanging N momenta with a scalar background field (ii) the "half-ladder" with N rungs in x - space (iii) the four-point ladder with N rungs in x - space as well as in (off-shell) momentum space. In each case we give a compact expression combining the N! Feynman diagrams contributing to the amplitude. As our main application, we reconsider the well-known case of two massive scalars interacting through the exchange of a massless scalar. Applying asymptotic estimates and a saddle-point approximation to the N-rung ladder plus crossed ladder diagrams, we derive a semi-analytic approximation formula for the lowest bound state mass in this model.Comment: 39 pages, 10 pdf figure

Computer Programs in Europe: A Comparative Analysis of the 1991 EC Software Directive

Long awaited – if not feared – in the computer industry, where its elaboration had evoked heated debate, the European Council Directive of May 14, 1991 on the Legal Protection of Computer Programs (the Directive or Software Directive )has imposed common principles of copyright protection on the twelve Member States of the European Community (the EC , the Community ). As it declares in its preamble, the Directive responds to the need to ensure the proper functioning of a single marketand, to that end, to eliminate man), of the current differences among the Member States\u27 legal systems. In the domain of European copyright law, the Software Directive is a trend-setting text. This, the Community\u27s first directive concerning copyright law, was enacted more than thirty years following the adoption of the Treaty of Rome. The treaty mentions copyright only in Article 36, which simply affirms that the free circulation of goods in the Community must respect intellectual property rights. The Directive was elaborated in the wake of the White Paper of 1985 on the internal market, which in turn presaged the adoption of the Single European Act of 1986, and followed the Green Paper of 1988 on Copyright and the Challenge of Technology. The White Paper mentioned intellectual property rights as objects of harmonization, especially with respect to new technologies, and the Green Paper constituted the first true program for Community action in the area of intellectual property. The historical contrast between the EC\u27s approach to copyright and that of the United States is striking. In the United States, the Constitution declared from the beginning federal competence over copyright law (and patent law), a competence which led to uniformity of law among the fifty States. The current EC effort shows that, starting from a diametrically opposed position, convergence can nonetheless occur. Henceforth, in Europe, Community institutions will take charge of at least some intellectual property issues, preempting or overriding Member State regulation in the field

Estimating the seed content of Vitis vinifera cv. Gewürztraminer berries by two parameters related with the fecundation process

The presence of a developed endosperm in a grape berry has been suggested to be a sufficient condition for berry set. The development of both, endosperm and embryo, leads to the formation of a seed and a grapevine flower usually contains 4 ovules. Taking this into account, a probabilistic approach has been used to study the seed content of Gewürztraminer berries in different plots in Alsace (France) over 7 years. The estimation of two probabilities, in relation with the development of the endosperm and the embryo, gives a good estimation of 5 variables (percentage of berries with 0 to 4 seeds). Knowing the number of flowers per shoot, this model explains 98 % of the variability of the number of berries per shoot and 99 % of the variability of the number of seeds per shoot between the years

Electroweak Baryogenesis with dimension-6 Higgs interactions

We present the computation of the baryon asymmetry in the SM amplified by dimension-6 Higgs interactions using the WKB approximation. Analyzing the one-loop potential it turns out that the phase transition is strongly first order in a wide range of the parameters. It is ensured not to wash out the net baryon number gained previously even for Higgs masses up to at least 170 GeV. In addition dimension-6 operators induce new sources of CP violation. Novel source terms which enhance the generated baryon asymmetry emerge in the transport equations. This model predicts a baryon to entropy ratio close to the observed value for a large part of the parameter space.Comment: 10 pages, 4 figures, Talk given at the 8th International Moscow School of Physic

The Euler-Heisenberg Lagrangian beyond one loop

We review what is presently known about higher loop corrections to the Euler-Heisenberg Lagrangian and its Scalar QED analogue. The use of those corrections as a tool for the study of the properties of the QED perturbation series is outlined. As a further step in a long-term effort to prove or disprove the convergence of the N photon amplitudes in the quenched approximation, we present a parameter integral representation of the three-loop Euler-Heisenberg Lagrangian in 1+1 dimensional QED, obtained in the worldline formalism.Comment: 11 pages, 2 figures, talk given by Christian Schubert at QFEXT11, Benasque, Spain, Sept. 18-24, 2011, to appear in the conference proceeding

Cryopreservation of encapsulated apices of sugarcane : effect of freezing procedure and histology

SUMMARY: The effect of sucrose concentration during the pregrowth treatment and of the freezing procedure on the survival of encapsulated apices of 6 sugarcane varieties was investigated. The optimal sucrose concentration was 0.75M. Survival was noted with both rapid freezing by direct immersion in liquid nitrogen and slow freezing using a programmable freezer but it was generally higher &er rapid cooling. Important genotypic variation was observed for both parameters studied. Histological examination revealed that cells were slightly harmed during pregrowth and freezing. Apices could withstand freezing as a whole. Direct regrowth of cryopreserved apices occurred within 3 days after thawing

Dynamic behaviour of an electrolyser with a two phase solid-liquid electrolyte : Part I : spectral analysis of potential fluctuations

The dynamic behaviour of a simplified electrolyser with a two phase solid-liquid electrolyte was investigated. The current-voltage curve and the impedance of the working electrode (current collector) was measured. In addition the fluctuations of the working electrode potential and of the electrolyte resistance close to the electrode were analysed, especially by spectral analysis. Conductive zinc-coated polystyrene beads and insulating glass beads were compared. For glass beads the kinetics were controlled by ohmic drop fluctuations due to the collisions of the beads onto the collector. With zinc beads the charge exchanges between the beads and the current collector were also observed and contributed to the potential fluctuations. A complementary analysis of the elementary potential and electrolyte resistance transients will be reported in Part II; the electrochemical behaviour of the collector will then be modelled

Nominal Unification of Higher Order Expressions with Recursive Let

A sound and complete algorithm for nominal unification of higher-order expressions with a recursive let is described, and shown to run in non-deterministic polynomial time. We also explore specializations like nominal letrec-matching for plain expressions and for DAGs and determine the complexity of corresponding unification problems.Comment: Pre-proceedings paper presented at the 26th International Symposium on Logic-Based Program Synthesis and Transformation (LOPSTR 2016), Edinburgh, Scotland UK, 6-8 September 2016 (arXiv:1608.02534