No description available.

Thèses (M.Sc.)--Université de Sherbrooke (Canada), 2003. / Titre de l'écran-titre (visionné le 20 juin 2006). Publié aussi en version papier.

Diss.--Politische Ökonomie--Leipzig, 1981. / Bibliogr. f. A 48-A 67.

Note:

Texte remanié de: Diss.--Rechtswissenschaft I--Universität Hamburg, 1992-1993. / Bibliogr. p. 229-237. Notes bibliogr. Index.

No description available.

Monopoles are solutions of an SU(2) gauge theory in R3 satisfying a lower bound for energy and certain asymptotic conditions, which translate as topological properties encoded in their charge. Using methods from integrable systems, monopoles can be described in algebraic-geometric terms via their spectral curve, i.e. an algebraic curve, given as a polynomial P in two complex variables, satisfying certain constraints. In this thesis we focus on the Ercolani-Sinha formulation, where the coefficients of P have to satisfy the Ercolani-Sinha constraints, given as relations amongst periods. In this thesis a particular class of such monopoles is studied, namely charge 3 monopoles with a symmetry by C3, the cyclic group of order 3. This class of cyclic 3-monopoles is described by the genus 4 spectral curve X , subject to the Ercolani-Sinha constraints: the aim of the present work is to establish the existence of such monopoles, which translates into solving the Ercolani-Sinha constraints for X . Exploiting the symmetry of the system,we manage to recast the problem entirely in terms of a genus 2 hyperelliptic curve X, the (unbranched) quotient of X by C3 . A crucial step to this aim involves finding a basis forH1( X; Z), with particular symmetry properties according to a theorem of Fay. This gives a simple formfor the period matrix of X ; moreover, results by Fay and Accola are used to reduce the Ercolani-Sinha constraints to hyperelliptic ones on X. We solve these constraints onX numerically, by iteration using the tetrahedral monopole solution as starting point in the moduli space. We use the Arithmetic-GeometricMean method to find the periods onX: this method iswell understood for a genus 2 curve with real branchpoints; in this work we propose an extension to the situation where the branchpoints appear in complex conjugate pairs, which is the case for X. We are hence able to establish the existence of a curve of solutions corresponding to cyclic 3-monopoles.

Let M = H³/Γ be a complete, non-compact, oriented geometrically finite hyperbolic 3-manifold without cusps. By constructing a conformal compactification of M x S¹ we functorially associate to M an oriented, conformally flat, compact 4-manifold X (without boundary) with an S¹-action. X determines M as a hyperbolic manifold. Using our functor and the differential geometry of conformally flat 4-manifolds we prove that any Γ as above with a limit set of Hausdorff dimension ≤ 1 is Schottky, Fuchsian or extended Fuchsian. Furthermore, the Hodge theory for H² (X;R) carries over to H¹(M, δM;R) and H²(M;R) which correspond to the spaces of harmonic L²-forms of degree 1 and 2 on M. Comparison of lattices through the Hodge star gives an invariant h(M) ε GL(H²(M;R)/GL(H²(M;Z)) of the hyperbolic structure. Secondly we pay attention to magnetic monopoles on M which correspond to S¹invariant solutions of the anti-self-duality equations on X. The basic result is that we associate to M an infinite collection of moduli spaces of monopoles , labelled by boundary conditions. We prove that the moduli spaces are not empty (under reasonable conditions), compute their dimension , prove orientability , the existence of a compactification and smoothness for generic S¹-invariant conformal structures on X. For these results one doesn't need a hyperbolic structure on M , the existence of a conformal compactification X suffices. A twistor description for monopoles on a hyperbolic M can be given through the twistor space of X , and monopoles turn out to correspond to invariant holomorphic bundles on twistor space. We analyse these bundles. Explicit formulas for monopoles can be found on handlebodies M , and for M = surface x R we describe the moduli spaces in some detail.

In 1931 P.A.M. Dirac postulated the existence of a quantum of magnetic charge, the magnetic monopole. Since its prediction, cosmic ray and accelerator experiments have been performed to detect the monopole, but all have failed. M. Ruderman and D. Zwanziger have put forward an explanation for the negative experimental results. They argue that monopoles are likely to be produced in pairs, which are tightly bound and never become free. Ruderman and Zwanziger point to certain anomalous cosmic ray events as evidence of production of bound monopole pairs. In this paper we review Dirac's arguments, calculate the monopole's properties, and critically review previous monopole experiments. Using the model proposed by Ruderman and Zwanziger to give identifying properties, we propose an experiment designed to detect the materialization of the magnetic monopole. / Master of Science

We investigate semiclassical contributions to correlation functions in N = 1 supersymmetric gauge theories. Our principal example is the gluino condensate, which signals the breaking of chiral symmetry, and should be exactly calculable, according to a persymmetric non-renormalisation theorem. However, the two calculational approaches previously employed, SCI and WCI methods, yield different values of the gluino condensate. We describe work undertaken to resolve this discrepancy, involving a new type of calculation in which the space is changed from R(^4) to the cylinder R(3) x S(1) This brings control over the coupling, and supersymmetry ensures that we are able to continue to large radii and extract answers relevant to R(^4). The dominant semiclassical configurations on the cylinder are all possible combinations of various types of fundamental monopoles. One specific combination is a periodic instanton, so monopoles are the analogue of the instanton partons that have been conjectured to be important at strong coupling. Other combinations provide significant contributions that are neglected in the SCI approach. Monopoles are shown to generate a superpotential that determines the quantum vacuum, where the theory is confining. The gluino condensate is calculated by summing the direct contributions from all fundamental monopoles. It is found to be in agreement with the WCI result for any classical gauge group, whereas the values for the exceptional groups have not been calculated before. The ADS superpotential, which describes the low energy dynamics of matter in a supersymmetric gauge theory, is derived using monopoles for all cases where instantons do not contribute. We report on progress made towards a two monopole calculation, in an attempt to quantify the missed contributions of the SCI method. Unfortunately, this eventually proved too complicated to be feasible.