Дисертації з теми "Yang Mills Higgs model"

The first part of this work deals with some new large N ideas for the YMH model in three dimensions. Needless to say there is a large historical and scientific background and it is of course difficult to say something really new on these subjects. Nevertheless some latest ideas on matrix models, subject on which I have worked in the first part of my period here at SISSA, are a valuable tool and should find applications in otherwise 'slow' fields. The study of large N model of monopole gas are not investigated, to our knowledge, for example. This work wants to be a starting point for this investigation. Along this analysis we have found many and different problems to think about, the principal is the reason how the Eguchi Kawai works, an issue that also has not been completely clarified, despite of the volume of numerical calculations. After one finds a reliable method for the functional determinant, it will be possible to draw definite conclusions on the large N monopole gas, which seems promising some interesting feature, due to the competition of factors which takes place in the large N limit.

Connus des mécaniciens de la géométrie de Poisson, les algébroïdes de Lie transitifs sont ici étudiés du point de vue de leurs sections afin de développer un formalisme algébrique plus proche de celui développé par les théories de jauge. Ici, les algébroïdes de Lie transitifs s'apparentent à une généralisation des champs de vecteurs sur la variété de base. Ce mémoire de thèse a pour objet l'étude des connexions généralisées sur les algébroïdes de Lie transitifs et la construction de théories de jauge. Les connexions ordinaires sur les algébroïdes de Lie transitifs sont définies par des 1-formes de connexion de l'algébroïde de Lie à valeurs dans son noyau et vérifiant une contrainte de normalisation sur ce noyau. En relâchant cette contrainte, on construit l'espace des 1-formes de connexions généralisées qui se décomposent, à l'aide d'une connexion ordinaire de fond, comme la somme d'une connexion ordinaire et d'un paramètre purement algébrique définit sur le noyau. Dans l'esprit des théories Yang-Mills, une action invariante de jauge est définie comme la “norme” de la courbure associée à une connexion généralisée. De cette action, il découle un lagrangien composé des termes des théories de jauge de type Yang-Mills-Higgs : le terme cinétique associé aux champs de jauge et le terme de couplage minimal pour un champ tensoriel scalaire plongé dans un potentiel quartique. La réduction du groupe de symétrie de la théorie s'effectue par une redistribution des degrés de liberté dans l'espace fonctionnel des champs de la théorie. Il résulte de ces manipulations la définition d'une théorie de type Yang-Mills dont les bosons vecteurs sont des champs massifs
Transitive Lie algebroids are usually studied from the point of view of the geometry of Poisson. Here, they are preferentially defined in terms of sections of fiber bundle in order to get close to the formalism of the gauge field theory. Then, transitive Lie algebroids can be seen as a generalization of vector fields on the base manifold. This PhD thesis is concerned with the study of generalized connections on transitive Lie algebroids and the construction of gauge theories. Ordinary connections on transitive Lie algebroids are defined as the subset of 1-forms on Lie algebroids with values in its kernel which fulfill a normalization constraint on this kernel. By relaxing this constraint, we build the space of generalized connection 1- forms. Using a background connection, we show that any generalized connections can be decomposed as the sum of an ordinary connection and a purely algebraic parameter defined on the kernel. As in Yang-Mills theories, we define a gauge invariant functional action as the “norm” of the curvature associated to a generalized connection. Then, the Lagrangian associated to this action forms a Yang-Mills-Higgs type model composed with the field strength associated to gauge fields and a minimal coupling with a tensorial scalar field embedded into a quartic potential. In the case of Atiyah Lie algebroids, the symmetry group of the theory can be reduced by using an appropriate rearrangement of the degrees of freedom in the functional space of fields. We thus obtain a Yang-Mills type theory describing massive vector bosons

This thesis is concerned with solitons (solutions of certain nonlinear partial differential equations) in certain cases when the underlying space is either a lattice or curved. Chapter 2 of the thesis is concerned with the outcome of collisions between a kink (a 1-dimensional soliton) and an antikink for certain topological discrete (TD) systems. The systems considered are the TD sine-Gordon and the TD ø(^4) For the TD sine-Gordon system it is found that the kink can support an internal shape mode which plays an important role during the collisions. In particular, this mode can be excited during collisions and this leads to spectacular resonance effects. The outcome of any particular collision has sensitive dependence on the initial conditions and could be either a trapped kink-antikink state, a "reflection" or a "transmission”. Such resonance effects are already known to exist for the conventional discrete ø(^4) system, and the TD ø(^4) system is no different, though the results for the two are not entirely similar. Chapter 3 considers the question of the existence of explicit travelling kink solutions for lattice systems. In particular, an expression for such a solution for the integrable lattice sine-Gordon system is derived. In Chapter 4, by reducing the Yang-Mills equations on the (2 + 2)-dimensional ultrahyperbolic space-time, an integrable Yang-Mills-Higgs system on (2 + 1) dimensional de Sitter space-time is derived. It represents the curved space-time version of the Bogomolny equations for monopoles on R(^3) . Using twister methods, various explicit solutions with gauge groups U(l) and SU(2) are constructed. A multi-solution SU(2) solution is also presented.

The notion of holomorphic vector bundle is common to some branches of mathematics and theoretical physics. In particular, such a notion seems to play a fundamental role in complex differential geometry, algebraic geometry and Yang-Mills theory. In this thesis we study a kind of holomorphic vector bundles over complex manifolds, known as Higgs bundles, and some of their main properties. We restrict such objects to the case when the complex manifold is compact Kähler. On one hand, complex manifolds provide a rich class of geometric objects, which behave rather differently than real smooth manifolds. For instance, one of the main characteristic of a compact complex manifold is that its group of biholomorphisms is always finite dimensional. On the other hand, since the manifolds in which we are interested are compact Kähler, we have that certain invariants associated with the holomorphic bundle can be defined using cohomology classes...

Cette thèse décrit quelques développements dans les techniques de calcul des amplitudes de diffusion en théorie supersymétrique de champ de jauge . L'accent est mis sur les relations de récurrence on-shell et sur l'utilisation de méthodes d'unitarité pour des calculs de boucle. En particulier, la récurrence on-shell est liée aux règles BCFW pour calculer les amplitudes de jauge au niveau des arbres. Les combinaisons de techniques de coupe d'unitarité et la récurrence sont utilisées pour calculer les amplitudes de boucle, et finalement, à partir des amplitudes, pour obtenir la fonction de corrélation énergie-énergie en théorie de super-Yang-Mills N = 4 à l'aide de la représentation de Mellin-Barnes. Dans le dernier chapitre, nous tentons de trouver un contour convergent pour les intégrales de Mellin Barnes en multi-dimension obtenu par une certaine approximation d'un contour de phase stationnaire.

The Yang-Mills-Higgs theory has its origins in Physics. It describes particles with masses via the Higgs mechanism and predicts magnetic monopoles. We study here the mathematical aspects of the theory following an analytical and geometric approach. Our motivation comes from physics and we work all the time with the full Lagrangian of the theory. At the same time, we are interested in it from the variational point of view, as a functional on an infinite dimensional space and as a system of non-linear equations on a non-compact manifold with finite energy as the only constraint. We are concerned mainly with the configuration space of the theory, the existence of solutions and their behaviour at infinity.

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Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
In this thesis, we are dedicated to study the time evolution generated by the hamiltonian of a classical Yang-Mills-Higgs theory with gauge symmetry SU(2) on a spatial lattice. In particular, we study energy transfer and equilibration processes among the gauge and Higgs sectors, calculate the maximal Liapunov exponents regarding to random initial conditions in the regime of weak coupling, where one expects them to be related to the high-temperature static plasmon damping rate, and investigate their energy and Higgs self-coupling parameter dependence. We further examine finite-time and finite-size errors, value the impact of the Higgs fields on the instabilty of constant non-abelian magnetic fields and comment on the implications of our obtained results for the thermalization properties of gauge fields at finite temperature in the presence of matter.

Orientador: Gastão Krein
Banca: Marcus Aloizio Martinez de Aguiar
Banca: Tobias Frederico
Banca: Sérgio Szpigel
Banca: Adriano Antonio Natale
Resumo: Nesta tese, dedicamo-nos a estudar a evolução temporal gerada pela hamiltoniana de uma teoria de Yang-Mills-Higgs clássica com simetria de calibre SU(2) em uma rede espacial. Em particular, estudamos transferência de energia e processos de equilibrção entre os setores de calibre e de Higgs, calculamos os expoentes de Liapunov máximos referentes a condições randômicas iniciais no regime de fraco acoplamento, onde espera-se que eles estejam relacionados à taxa de amortecimento estático do plasmon a alta temperatura, e investigamos sua dependência com a energia e o parâmetro de auto-acoplamento de Higgs. Examinamos ainda erros de tamanho finito e de tempo finito, avaliamos o impacto dos campos de Higgs na instabilidade de campos magnéticos não-abelianos constantes e comentamos as implicações dos nossos resultados obtidos para as propriedades de termalização de campos de calibre a temperatura finita na presença de matéria.
Abstract: In this thesis, we are dedicated to study the time evolution generated by the hamiltonian of a classical Yang-Mills-Higgs theory with gauge symmetry SU(2) on a spatial lattice. In particular, we study energy transfer and equilibration processes among the gauge and Higgs sectors, calculate the maximal Liapunov exponents regarding to random initial conditions in the regime of weak coupling, where one expects them to be related to the high-temperature static plasmon damping rate, and investigate their energy and Higgs self-coupling parameter dependence. We further examine finite-time and finite-size errors, value the impact of the Higgs fields on the instabilty of constant non-abelian magnetic fields and comment on the implications of our obtained results for the thermalization properties of gauge fields at finite temperature in the presence of matter.
Doutor

Dissertação (mestrado) - Universidade Federal de Santa Catarina, Centro de Ciências Físicas e Matemáticas. Programa de Pós-graduação em Física
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Monopolos magnéticos têm sido objetos de grande interesse nos últimos anos, principalmente por serem previstos em algumas teorias de grande unificação e por, possivelmente, serem relevantes no fenômeno do confinamento em QCD. Consideramos uma teoria de Yang-Mills-Higgs com simetria de gauge SU(n) quebrada espontaneamente em SO(n) que apresenta condições topológicas necessárias para a existência de monopolos Z2. Construímos as formas assintóticas desses monopolos, considerando duas quebras distintas do SU(n) em SO(n), e verificamos que os monopolos fundamentais estão associados aos pesos da representação definidora da álgebra so(n)v.

Ma thèse porte sur la dynamique des champs de Higgs, dans leurs aspects géométriques classiques et supersymétriques. Dans une première partie, qui a donné lieu à une publication dans la revue « Journal of Geometry and Physics », numéro 57, 2007, je suis parti du point de vue classique de Kaluza Klein. En considérant une théorie de gravitation d'Einstein sur un espace-temps élargi fibre en espaces homogènes compacts G/H au-dessus de l'espace-temps ordinaire, j'ai défini pour la théorie réduite un espace affine F de champs scalaires cet espace provient d'un sous-ensemble des métriques sur les fibres, il est naturellement associé à une décomposition de la restriction à H de la représentation adjointe de G ; en restriction à F le potentiel est positi et coercitif et les couplages des champs scalaires avec la gravité réduite ainsi qu'avec la théorie de Yang-Milh réduite possèdent toutes les propriétés des champs de Higgs standard. Il se trouve que dans tous les cas le potentiel sur F est une fonction polynômiale de degré inférieur ou égal à 6. Ce potentiel peut donner naissance à de nouveaux types de monopoles. La seconde partie de la thèse étudie les champs obtenus en compactifiant une théorie de super-gravité, à la manière de Cremmer-Julia-Scherk , Duff ou DeWit -Nicolai. En premier lieu j'ai repris la formulation des théories de super-gravité en super-espace suivant Salam et Strathdee, comme elle est exposée dans Wess et Bagger, mais en dimension arbitraire ; j'ai trouvé une interprétation géométrique des contraintes de torsions en supergravité : en adoptant le point de vue de John Lott où le groupe de Lorentz est augmenté, mais en considérant l'extension affine du groupe de jauge, ces contraintes traduisent l'existence d'une jauge où l'action sur le vielbein des super-difféomorphismes coïncide avec celle des super-translations de jauge. Parallèlement, j'ai repris la théorie des lagrangiens supersymétriques en restant systématiquement dans la catégorie des supervariétés équivalente à celle des faisceaux de Berezin et Kostant ; j'ai ainsi obtenu des équations nouvelles de champs classiques de spineurs, dans le cas des « supergéodésiques », des « supersigma-modèles » et de « super-Yang-Mills ». Ceci forme un chapitre autonome de la thèse, qui introduit à la dernière partie : Reconsidérer les potentiels des champs scalaires définis par DeWit et Nicolai pour les théories de super gravité jaugées d'espèce N=8 en dimension 4. Ces théories sont équivalentes à des compactifications sur de; sphères de dimension 7 de la super-gravité étendue en dimension 11, selon Cremmer, Julia, Scherk et DeWi Nicolai elles possèdent une invariance globale sous un groupe réel exceptionnel E7 et leurs champs scalaires sont à valeurs dans un espace homogène E7(7)/SU(8). J'étudie les relations de ce potentiel avec les constructions de la première partie appliquées au groupe SO(8)xSO(8)
My thesis concerns Higgs fields dynamics, in their classical geometrical and supersymmetrical aspects. In a first part which has given rise to a publication in the "Journal of Geometry and Physics", volume 57 (2007), I have started from the classical Kaluza-Klein point of view. Considering an Einstein gravitational theory on an extended spacetime, fibered with homogeneous spaces G/H over the ordinary spacetime, I defined for the reduced theory an affine space F of scalar fields; this space cornes from a subset of metrics in the fibers, it is naturally associated to the decomposition of the restriction to H of the adjoint representation of G. When restricted to F, the potential is positive and coercitive, and the couplings of the scalar fields with the reduced gravity as well as with Yang-Mills reduced theory possess all standard Higgs fields properties. It appears in this case that the potential on F is a polynomial function with degree smaller or equal to 6. This potential may give rise to new types of monopoles. The second part of the thesis concerns the study of the fields obtained by compactifying a supergravity theory, in the way of Cremmer-Julia-Scherk, Duff, or DeWit and Nicolai. In a first step, I reconsidered the formulation of supergravity theories in superspace, following Salam and Strathdee, as it is exposed in Wess and Bagger, but in arbitrary dimension; I hâve found a geometrical interpretation of the torsion constraints in supergravity: adopting the point of view of John Lott where the Lorentz group is extended, but considering the affine extension of the gauge group, these constraints express the existence of a gauge where the action on the supervielbein of superdiffeomorphisms is équivalent to the action of gauge supertranslations. In parallel, I reconsidered supersymmetric Lagrangian theory while staying systematically in the category of supermanifolds that is equivalent to that of the scheaves of Berezin and Kostant; I thus obtained new classical spinorfield equations, in the case of "super-geodesics", "super-sigma-models", and "super-Yang-Mills". This is an independent chapter of the thesis, which introduces the last part: reconsidering the scalar fields potentiels defined by DeWit and Nicolai for gauged N=8 supergravities in 4 dimensions. These theories are equivalent to seven-sphere compactifications of eleven-dimensional supergravity. From Cremmer, Julia, DeWit and Nicolai, they possess global invariance under a real exceptional E7 group and the scalar fields take their values in a homogeneous space E7(7)/ SU(8). I study the relations of this potential with the constructions of the first part applied to the group SO(8)xSO(8)

In this work aspects of the classical Connes-Lott non-commutative standard model are examined. In particular the relationship between the chiral structure of the standard model and the condition of Poincaré Duality is investigated. Then the natural prediction of an additional force in the non-commutative standard model is explained and the consequences calculated. Finally the attempts at grand unification within the non-commutative framework are reviewed and extended.

acase@tulane.edu
The Bohr-Mottelson collective model is central to the study of nuclear structure physics. The model treats nuclei as ellipsoids and focuses on their vibrational and rotational degrees of freedom. The rotational part of the model regards the moment of inertia of the nuclei as a falling between the extreme of a rigid body and an irrotational fluid. The true moment of inertia, as revealed by experiment, provides a parameter between these two extremes and acts as a way of interpolating the data. In this work, we show how the interpolating parameter between the two extreme moments of inertia can be treated theoretically using an algebraic and differential geometric framework. The essential idea is to couple the angular momentum of the nucleus with a ``magnetic" term that involves the Kelvin circulation into a covariant derivative. This coupling term or connection can be found by solving a Yang-Mills equation. Measuring the nuclear Kelvin circulation then reveals a theoretical justification for the determining the correct moment of inertia.
1
Nick Sparks

Mode of access: World Wide Web.
Thesis (Ph. D.)--University of Hawaii at Manoa, 2004.
Includes bibliographical references (leaves 159-164).
Electronic reproduction.
Also available by subscription via World Wide Web
x, 164 leaves, bound ill. 29 cm

This thesis investigates the possibility that the gauge boson in a certain hypothetical SU(2) gauged sector can constitute all the non-baryonic dark matter. The gauge bosons acquire mass from the Higgs mechanism as in the Standard Model and scatter elastically among themselves non-gravitationally. It is expected that this self interaction of the dark gauge bosons would resolve the various discrepancies between the ΛCDM model and astrophysical observations on small (e.g. galactic or galaxy cluster) scales. Parameter space within the domain of validity of perturbation theory satisfying the constraints of dark matter abundance, the elastic self-scattering momentum transfer cross-section suggested by recent astrophysical observations, and consideration of the Big-Bang nucleosynthesis was found to be non-empty in the “forbidden” regime where the mass of the dark Higgs boson is greater than the mass of the dark gauge boson.
Graduate