Analyzing dynamical gluon mass generation

We study the necessary conditions for obtaining infrared finite solutions from the Schwinger-Dyson equation governing the dynamics of the gluon propagator. The equation in question is set up in the Feynman gauge of the background field method, thus capturing a number of desirable features. Most notably, and in contradistinction to the standard formulation, the gluon self-energy is transverse order-by-order in the dressed loop expansion, and separately for gluonic and ghost contributions. Various subtle field-theoretic issues, such as renormalization group invariance and regularization of quadratic divergences, are briefly addressed. The infrared and ultraviolet properties of the obtained solutions are examined in detail, and the allowed range for the effective gluon mass is presented.

Fatores de forma eletromagnéticos do píon e do káon na frente de luz

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Experimentos mentais no ensino de ciências: implementação de uma sequência didática

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Integração em dimensões negativas em calibres covariantes e não-covariantes

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Métodos de ressoma no super-espaço aplicados ao modelode O’Raifeartaigh

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Zeros of classical orthogonal polynomials of a discrete variable

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Correspondence between the one-loop three-point vertex and the Y and Delta electric resistor networks

Different mathematical methods have been applied to obtain the analytic result for the massless triangle Feynman diagram yielding a sum of four linearly independent (LI) hypergeometric functions of two variables F-4. This result is not physically acceptable when it is embedded in higher loops, because all four hypergeometric functions in the triangle result have the same region of convergence and further integration means going outside those regions of convergence. We could go outside those regions by using the well-known analytic continuation formulas obeyed by the F-4, but there are at least two ways we can do this. Which is the correct one? Whichever continuation one uses, it reduces a number of F-4 from four to three. This reduction in the number of hypergeometric functions can be understood by taking into account the fundamental physical constraint imposed by the conservation of momenta flowing along the three legs of the diagram. With this, the number of overall LI functions that enter the most general solution must reduce accordingly. It remains to determine which set of three LI solutions needs to be taken. To determine the exact structure and content of the analytic solution for the three-point function that can be embedded in higher loops, we use the analogy that exists between Feynman diagrams and electric circuit networks, in which the electric current flowing in the network plays the role of the momentum flowing in the lines of a Feynman diagram. This analogy is employed to define exactly which three out of the four hypergeometric functions are relevant to the analytic solution for the Feynman diagram. The analogy is built based on the equivalence between electric resistance circuit networks of types Y and Delta in which flows a conserved current. The equivalence is established via the theorem of minimum energy dissipation within circuits having these structures.

Three-point functions and su(1 vertical bar 1) spin chains

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

The Epstein-Glaser causal approach to the light-front QED(4). I: Free theory

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

On the question of neutrino spin precession in a magnetic field

Using the Feynman procedure of ordered exponential operators we solve the evolution equations for a two-neutrino system considering arbitrarily varying matter density and magnetic field along the neutrino trajectory. We show that a large geometrical phase velocity suppresses νL→νR transitions unless some stationary trajectory is found along the neutrino path. Concerning the solar neutrino case, if we admit the standard solar model matter distribution, no such trajectory can be found.

Perturbative super-Yang-Mills from the topological AdS 5 × S 5 sigma model

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Método de integração em dimensão negativa em teoria quântica de campos

This work is a review of the Negative Dimension Integration Method as a powerful tool for the computation of the radiative corrections present in Quantum Field Perturbation Theory. This method is applicable in the context of Dimensional Regularization and it provides exact solutions for Feynman integrals with both dimensional parameter and propagator exponents generalized. These solutions are presentedintheformoflinearcombinationsofhypergeometricfunctionswhosedomains of convergence are related to the analytic structure of the Feynman Integral. Each solution is connected to the others trough analytic continuations. Besides presenting and discussing the general algorithm of the method in a detailed way, we offer concrete applications to scalar one-loop and two-loop integrals as well as to the one-loop renormalizationofQuantumElectrodynamics (QED)

Supersymmetric Dark Matter : aspects of sfermion coannihilations

There is very strong evidence that ordinary matter in the Universe is outweighed by almost ten times as much so-called dark matter. Dark matter does neither emit nor absorb light and we do not know what it is. One of the theoretically favoured candidates is a so-called neutralino from the supersymmetric extension of the Standard Model of particle physics. A theoretical calculation of the expected cosmic neutralino density must include the so-called coannihilations. Coannihilations are particle processes in the early Universe with any two supersymmetric particles in the initial state and any two Standard Model particles in the final state. In this thesis we discuss the importance of these processes for the calculation of the relic density. We will go through some details in the calculation of coannihilations with one or two so-called sfermions in the initial state. This includes a discussion of Feynman diagrams with clashing arrows, a calculation of colour factors and a discussion of ghosts in non-Abelian field theory. Supersymmetric models contain a large number of free parameters on which the masses and couplings depend. The requirement, that the predicted density of cosmic neutralinos must agree with the density observed for the unknown dark matter, will constrain the parameters. Other constraints come from experiments which are not related to cosmology. For instance, the supersymmetric loop contribution to the rare b -> sγ decay should agree with the measured branching fraction. The principles of the calculation of the rare decay are discussed in this thesis. Also on-going and planned searches for cosmic neutralinos can constrain the parameters. In one of the accompanying papers in the thesis we compare the detection prospects for several current and future searches for neutralino dark matter.

Jarrow-Yildirim model for inflation: theory and applications

This thesis deals with inflation theory, focussing on the model of Jarrow & Yildirim, which is nowadays used when pricing inflation derivatives. After recalling main results about short and forward interest rate models, the dynamics of the main components of the market are derived. Then the most important inflation-indexed derivatives are explained (zero coupon swap, year-on-year, cap and floor), and their pricing proceeding is shown step by step. Calibration is explained and performed with a common method and an heuristic and non standard one. The model is enriched with credit risk, too, which allows to take into account the possibility of bankrupt of the counterparty of a contract. In this context, the general method of pricing is derived, with the introduction of defaultable zero-coupon bonds, and the Monte Carlo method is treated in detailed and used to price a concrete example of contract. Appendixes: A: martingale measures, Girsanov's theorem and the change of numeraire. B: some aspects of the theory of Stochastic Differential Equations; in particular, the solution for linear EDSs, and the Feynman-Kac Theorem, which shows the connection between EDSs and Partial Differential Equations. C: some useful results about normal distribution.

Ein, zwei Punkte zu Nichtkommutativer Geometrie und Quantenfeldtheorie auf diskreten Räumen

Über viele Jahre hinweg wurden wieder und wieder Argumente angeführt, die diskreten Räumen gegenüber kontinuierlichen Räumen eine fundamentalere Rolle zusprechen. Unser Zugangzur diskreten Welt wird durch neuere Überlegungen der Nichtkommutativen Geometrie (NKG) bestimmt. Seit ca. 15Jahren gibt es Anstrengungen und auch Fortschritte, Physikmit Hilfe von Nichtkommutativer Geometrie besser zuverstehen. Nur eine von vielen Möglichkeiten ist dieReformulierung des Standardmodells derElementarteilchenphysik. Unter anderem gelingt es, auch denHiggs-Mechanismus geometrisch zu beschreiben. Das Higgs-Feld wird in der NKG in Form eines Zusammenhangs auf einer zweielementigen Menge beschrieben. In der Arbeit werden verschiedene Ziele erreicht:Quantisierung einer nulldimensionalen ,,Raum-Zeit'', konsistente Diskretisierungf'ur Modelle im nichtkommutativen Rahmen.Yang-Mills-Theorien auf einem Punkt mit deformiertemHiggs-Potenzial. Erweiterung auf eine ,,echte''Zwei-Punkte-Raum-Zeit, Abzählen von Feynman-Graphen in einer nulldimensionalen Theorie, Feynman-Regeln. Eine besondere Rolle werden Termini, die in derQuantenfeldtheorie ihren Ursprung haben, gewidmet. In diesemRahmen werden Begriffe frei von Komplikationen diskutiert,die durch etwaige Divergenzen oder Schwierigkeitentechnischer Natur verursacht werden könnten.Eichfixierungen, Geistbeiträge, Slavnov-Taylor-Identität undRenormierung. Iteratives Lösungsverfahren derDyson-Schwinger-Gleichung mit Computeralgebra-Unterstützung,die Renormierungsprozedur berücksichtigt.