Die gibbs'sche erscheinung in der theorie der kugelfunktionen

n/

Mathematical lectures

Lectures delivered at the Rice Institute, May 20, 22, and 23, 1929, by Hermann Weyl, Ph.D., Professor of Mathematics at the Technische Hochschule in Zurich.I. Consistency in mathematics -- II. The spherical symmetry of atoms -- III. Gravitation and the electro

Thermodynamic of Distorted Reissner-Nordstr\"om Black Holes in Five-dimensions

In this paper, we study mechanics and thermodynamics of distorted, five-dimensional, electrically charged (non-extremal) black holes on the example of a static and "axisymmetric" black hole distorted by external, electrically neutral matter. Such a black hole is represented by the derived here solution of the Einstein-Maxwell equations which admits an $\mathbb{R}^1\times U(1)\times U(1)$ isometry group. We study the properties of this distorted black hole.Comment: 7 pages, submitted for the proceedings of the First Karl Schwarzschild Meeting (Frankfurt, 2013

Comptes rendus sur Dingler, Physik und Hypothese (1921)

Cette section contient les recensions que Rudolf Carnap, Moritz Schlick et Hermann Weyl ont données de l’ouvrage de Hugo Dingler : Physik und Hypothese. Versuch einer induktiven Wissenschaftslehre nebst einer kris­tischen Analyse der Fundamente der Relativitätstheorie [Dingler 1921]. Elles sont traduites par Christophe Bouriau en collaboration avec Oliver Sehlaudt et Gerhard Heinzmann.In this section one finds reviews of Hugo Dingler’s Physik und Hypothese, Versuch einer induktiven Wissenschaftslehre nebst einer kristi­schen Analyse der Fundamente der Relativitätstheorie [Dingler 1921], transla­ted by Christophe Bouriau in collaboration with Oliver Sehlaudt and Gerhard Heinzmann

Teaching Theoretical Physics: the cases of Enrico Fermi and Ettore Majorana

We report on theoretical courses by Fermi and Majorana, giving evidence of the first appearance and further development of Quantum Mechanics teaching in Italy. On the basis of original documents, we make a comparison between Fermi's and Majorana's approaches. A detailed analysis is carried out of Fermi's course on Theoretical Physics attended by Majorana in 1927-28. Three (previously unknown) programs on advanced Physics courses submitted by Majorana to the University of Rome between 1933 and 1936 and the course he held in Naples in 1938 complete our analysis: Fermi's phenomenological approach resounded in Majorana, who however combined it with a deeper theoretical approach, closer to the modern way of presenting Quantum Mechanics.Comment: latex, 21 pages; a contribution in the centenary of the birth of Ettore Majoran

Canonical Structure of Classical Field Theory in the Polymomentum Phase Space

Canonical structure of the space-time symmetric analogue of the Hamiltonian formalism in field theory based on the De Donder-Weyl (DW) theory is studied. In $n$ space-time dimensions the set of $n$ polymomenta is associated to the space-time derivatives of field variables. The polysymplectic $(n+1)$-form generalizes the simplectic form and gives rise to a map between horizontal forms playing the role of dynamical variables and vertical multivectors generalizing Hamiltonian vector fields. Graded Poisson bracket is defined on forms and leads to the structure of a Z-graded Lie algebra on the subspace of the so-called Hamiltonian forms for which the map above exists. A generalized Poisson structure arises in the form of what we call a ``higher-order'' and a right Gerstenhaber algebra. Field euations and the equations of motion of forms are formulated in terms of the graded Poisson bracket with the DW Hamiltonian $n$-form H\vol (\vol is the space-time volume form and $H$ is the DW Hamiltonian function). A few applications to scalar fields, electrodynamics and the Nambu-Goto string, and a relation to the standard Hamiltonian formalism in field theory are briefly discussed. This is a detailed and improved account of our earlier concise communications (hep-th/9312162, hep-th/9410238, and hep-th/9511039).Comment: 45 pages, LaTeX2e, to appear in Reports on Mathematical Physics v. 41 No. 1 (1998

The unexpected resurgence of Weyl geometry in late 20-th century physics

Weyl's original scale geometry of 1918 ("purely infinitesimal geometry") was withdrawn by its author from physical theorizing in the early 1920s. It had a comeback in the last third of the 20th century in different contexts: scalar tensor theories of gravity, foundations of gravity, foundations of quantum mechanics, elementary particle physics, and cosmology. It seems that Weyl geometry continues to offer an open research potential for the foundations of physics even after the turn to the new millennium.Comment: Completely rewritten conference paper 'Beyond Einstein', Mainz Sep 2008. Preprint ELHC (Epistemology of the LHC) 2017-02, 92 pages, 1 figur

Force, charge, and conductance of an ideal metallic nanowire

The conducting and mechanical properties of a metallic nanowire formed at the junction between two macroscopic metallic electrodes are investigated. Both two- and three-dimensional wires with a W(ide)-N(arrow)-W(ide) geometry are modelled in the free-electron approximation with hard-wall boundary conditions. Tunneling and quantum-size effects are treated exactly using the scattering matrix formalism. Oscillations of order E_F/lambda_F in the tensile force are found when the wire is stretched to the breaking point, which are synchronized with quantized jumps in the conductance. The force and conductance are shown to be essentially independent of the width of the wide sections (electrodes). The exact results are compared with an adiabatic approximation; the later is found to overestimate the effects of tunneling, but still gives qualitatively reasonable results for nanowires of length L>>lambda_F, even for this abrupt geometry. In addition to the force and conductance, the net charge of the nanowire is calculated and the effects of screening are included within linear response theory. Mesoscopic charge fluctuations of order e are predicted which are strongly correlated with the mesoscopic force fluctuations. The local density of states at the Fermi energy exhibits nontrivial behavior which is correlated with fine structure in the force and conductance, showing the importance of treating the whole wire as a mesoscopic system rather than treating only the narrow part.Comment: 23 pages, 8 figure

Searching for Higgs : From LEP towards LHC

After a brief introduction to the theoretical basis of the Higgs mechanism for generating the masses of elementary particles, the experimental searches for Higgs particles will be summarized, from bounds at LEP to inferences for LHC. The report will focus on the Standard Model, though some central results on extended Higgs systems, as conjectured for example in supersymmetric theories, will also be recapitulated. Alternative scenarios based on spontaneous symmetry breaking by novel strong interactions are adumbrated at the theoretical level.Comment: Added reference