Probing the ground state in gauge theories

We consider two very different models of the flux tube linking two heavy quarks: a string linking the matter fields and a Coulombic description of two separately gauge invariant charges. We compare how close they are to the unknown true ground state in compact U(1) and the SU(2) Higgs model. Simulations in compact U(1) show that the string description is better in the confined phase but the Coulombic description is best in the deconfined phase; the last result is shown to agree with analytical calculations. Surprisingly in the non-abelian theory the Coulombic description is better in both the Higgs and confined phases. This indicates a significant difference in the width of the flux tubes in the two theories.Comment: 13 pages, 10 .eps figures. V2: conclusions extende

Mathematical surprises and Dirac's formalism in quantum mechanics

By a series of simple examples, we illustrate how the lack of mathematical concern can readily lead to surprising mathematical contradictions in wave mechanics. The basic mathematical notions allowing for a precise formulation of the theory are then summarized and it is shown how they lead to an elucidation and deeper understanding of the aforementioned problems. After stressing the equivalence between wave mechanics and the other formulations of quantum mechanics, i.e. matrix mechanics and Dirac's abstract Hilbert space formulation, we devote the second part of our paper to the latter approach: we discuss the problems and shortcomings of this formalism as well as those of the bra and ket notation introduced by Dirac in this context. In conclusion, we indicate how all of these problems can be solved or at least avoided.Comment: Largely extended and reorganized version, with new title and abstract and with 2 figures added (published version), 54 page

European Constitution and National Constitution

Preface "The history of the question of alliance, integration, and unification of European states along different lines reaches far back. We only have to mention I. Kant and J. C. Bluntschli, who saw the future of Europe in establishing a union of its states based on the rule of law. It was on the grounds of freedom and republican democracy that J. Lorimer of Edinburgh envisaged the possibility of uniting European states. Much like him, Polish thinkers too, including A. Mickiewicz, B. Limanowski, and K. Kelles-Krauz, believed that Europe would unite as soon as its constituent states were driven by shared ideals of freedom and republican democracy."(...

SEMICLASSICAL AND QUANTUM MECHANICAL TREATMENTS OF POSITIVE AND NEGATIVE ANGLE POLARIZED HEAVY ION SCATTERING

Nous utilisons une théorie semiclassique pour calculer les sections efficaces et les pouvoirs d'analyse à tout ordre en diffusion élastique d'ions lourds polarisés. Cette approche a pour but d'expliquer les déviations par rapport à l'absence de structure observée normalement dans les sections efficaces. Ces déviations sont dues aux interférences entre diffraction et réfraction. Nous montrons que la diffusion réfractive à angle négatif ("farside scattering") peut être interprétée comme un effet de taille de la cible à Elab ≈ 20 MeV pour [MATH]Li + 12C. Il est montré que le très grand nombre d'intégrales à calculer numériquement 1imite le champ d'application de la méthode semiclassique. Finalement nous présentons une approche quantique pour traiter la diffusion à angles positifs et négatifs.A unified semiclassical theory for calculating cross section and analysing powers of al1 ranks for polarized heavy ion elastic scattering is applied to explain deviations from the structureless pattern normally encountered in the cross section, which are interpreted as due to interference between diffraction and refraction. Refractive, negative angle or far-side scattering is then discussed and is shown to be a target-size effect at Elab ≈ 20 MeV for [MATH]Li + 12C. The limitations of the semiclassical method are then shown in terms of the necessity of performing a huge number of integrals numerically. Lastly, a quantum mechanical approach for handling positive and negative angle scattering is presented

Wave propagation in a waveguide with a balance of gain and loss

A waveguide problem with a balance between loss and gain has been defined by one of the authors in the COST 240, Working Group 2, to study the mode behaviour in the case of complex refractive index and to compare different approaches. Peculiar wave properties of a waveguide with a balance of gain and loss are described and used to formulate a new beam propagation method (BPM) benchmark test