Este trabalho é resultado de uma série de estudos feitos com o objetivo de investigar a influ- ência de uma álgebra fermiônica deformada nos mecanismos de quebra e restauração da si- metria quiral no modelo de Nambu-Jona-Lasinio. Esse modelo foi escolhido pois é um modelo efetivo para a QCD que mostra com razoável facilidade uma de suas principais características, a quebra dinâmica da simetria quiral e a geração de uma massa dinâmica para os quarks. O trabalho pode ser dividido essencialmente em três partes. A primeira consiste em um estudo inicial onde a deformação foi implementada diretamente na equação de gap do modelo NJL através de um cálculo deformado do condensado. Na segunda parte, o mesmo procedimento de deformação foi aplicado na Hamiltoniana do modelo permitindo que seus efeitos se propagem nos cálculos até uma nova equação de gap. Uma extensão natural do trabalho e um estudo do modelo deformado a temperatura finita, onde a coexistência da temperatura e da deformação algébrica pode ser investigada. Esse estudo e a terceira parte do trabalho / This work is a result of a serie of studies where the aim is to investigate the influence of a de- formed fermionic algebra in the mechanisms of breaking and restoration of chiral symmetry in the Nambu-Jona-Lasinio model. This model was chosen because it is an effective model for QCD which shows with reasonable facility one of its main features, the dynamical breaking of chiral symmetry and the generation of a dynamical mass for the quarks. The work can be divided essentialy in three parts. The first consists in a initial study where the deformation was implemented directly in the gap equation of the NJL model through a defor- med calculation of the condensates. In second part, the same deformation procedure was applied in the Hamiltonian of the model allowing their effects to be propagated in the calcula- tions till a new gap equation. A natural extension of the work is a study of the deformed model at finite temperature, where the coexistence of temperature and algebric deformation can be investigated. This study is the third part of the work.

Este trabalho é resultado de uma série de estudos feitos com o objetivo de investigar a influ- ência de uma álgebra fermiônica deformada nos mecanismos de quebra e restauração da si- metria quiral no modelo de Nambu-Jona-Lasinio. Esse modelo foi escolhido pois é um modelo efetivo para a QCD que mostra com razoável facilidade uma de suas principais características, a quebra dinâmica da simetria quiral e a geração de uma massa dinâmica para os quarks. O trabalho pode ser dividido essencialmente em três partes. A primeira consiste em um estudo inicial onde a deformação foi implementada diretamente na equação de gap do modelo NJL através de um cálculo deformado do condensado. Na segunda parte, o mesmo procedimento de deformação foi aplicado na Hamiltoniana do modelo permitindo que seus efeitos se propagem nos cálculos até uma nova equação de gap. Uma extensão natural do trabalho e um estudo do modelo deformado a temperatura finita, onde a coexistência da temperatura e da deformação algébrica pode ser investigada. Esse estudo e a terceira parte do trabalho / This work is a result of a serie of studies where the aim is to investigate the influence of a de- formed fermionic algebra in the mechanisms of breaking and restoration of chiral symmetry in the Nambu-Jona-Lasinio model. This model was chosen because it is an effective model for QCD which shows with reasonable facility one of its main features, the dynamical breaking of chiral symmetry and the generation of a dynamical mass for the quarks. The work can be divided essentialy in three parts. The first consists in a initial study where the deformation was implemented directly in the gap equation of the NJL model through a defor- med calculation of the condensates. In second part, the same deformation procedure was applied in the Hamiltonian of the model allowing their effects to be propagated in the calcula- tions till a new gap equation. A natural extension of the work is a study of the deformed model at finite temperature, where the coexistence of temperature and algebric deformation can be investigated. This study is the third part of the work.

O objetivo principal desta dissertação é estudar a ressonância $\\k$, um méson escalar ainda hoje bastante controverso na comunidade científica. Estudamos o espalhamento elástico $K\\pi$, pois é neste subsistema que o $\\k$ se manifesta como um estado intermediário. A partir de uma lagrangiana efetiva quiral $SU(3)\\times SU(3)$, envolvendo termos de contato e ressonâncias, calculamos a amplitude $K\\pi$ projetada no canal de isospin $1/2$ e em seguida a unitarizamos por meio de {\\it loops} mesônicos. Investigamos os pólos físicos da amplitude, dados pelos zeros do seu denominador que se encontram na segunda superfície de Riemann. Esses zeros podem ser obtidos numericamente, mas a análise estrita desta solução não fornece informações a respeito da dinâmica que produz os pólos. Como alternativa, uma descrição qualitativa dos pólos foi obtida considerando o limite de $SU(2) \\Leftrightarrow M_\\p=0$ e a aproximação da matriz K, que corresponde a unitarizar a amplitude com {\\it loops} de $K\\p$ na camada de massa. Essas simplificações reduzem o denominador da amplitude a um polinômio de segundo grau, que dá origem a dois pólos físicos, posteriormente identificados como sendo o $K^*_0(1430)$ e o $\\k$. Este modelo simplificado permite uma boa interpretação da origem dinâmica dos pólos. O $\\k$ mostrou-se estável na variação dos acoplamentos da ressonância explícita, o que indica que ele é produzido pelo diagrama de contato. Já a ressonância identificada como o $K^*_0(1430)$ varia de um estado ligado a um pólo não físico, dependendo dos valores atribuídos aos parâmetros da ressonância, o que sugere fortemente que a natureza destes pólos é distinta. Esses diferentes comportamentos dinâmicos também foram observados no programa numérico, indicando que a essência dos pólos foi mantida no modelo simplificado. % Com o programa numérico obtivemos a posição do pólo do $\\k$ em $(0.7505 \\pm 0.0010) - i\\, (0.2363 \\pm 0.0023)\\;$GeV, o que está em pleno acordo com diversos modelos quirais muito mais complicados. / This work aims mostly at studying the $\\k$ resonance, which is still a controversial scalar meson nowadays within the scientific community. We studied the $K\\pi$ elastic scattering, because the $\\k$ appears as an intermediate state in this subsystem. From an effective chiral lagrangian $SU(3)\\times SU(3)$, involving contact terms and resonances, we calculated the $K\\pi$ amplitude projected on the $1/2$ isospin channel and then unitarized by means of mesonic {\\it loops}. The physical poles of the amplitude were investigated, given by the zeros of its denominator which are encountered on the Riemanns surface. Although these zeros can be numerically obtained, the strict analysis of this solution does not supply information about the poles producing dynamics. Alternatively, a qualitative description of the poles was obtained considering the $SU(2) \\Leftrightarrow M_\\p=0$ limit and the K matrix approximation, which corresponds to the unitarizing of the amplitude with {\\it loops} of $K\\p$ on shell. These simplifications reduce the amplitude denominator to a second grade polynomial that originates two physical poles, later identified as being $K^*_0(1430)$ and $\\k$. This simplified model allows for a good interpretation of the poles dynamic origin. The $\\k$ has been stable on the explicit resonance coupling, showing that it is produced by the contact diagram. The $K^*_0(1430)$ identified resonance, on the other hand, varies from a bounded state to a non-physical pole, depending on the resonance parameters attributed values, which strongly suggest that the nature of this poles is distinct. These different dynamic behaviors have also been observed in the numerical programs, indicating that the essence of the poles was maintained in the simplified model. With the numerical programs we obtained the position of pole $\\k$ in $(0.7505 \\pm 0.0010) - i\\, (0.2363 \\pm 0.0023)\\;$GeV, which is in accordance with various more complex chiral models.

<p>One of the still big problems in the Standard Model of particle physics is the problem of confinement. Quarks or other coloured particles have never been observed in isolation. Quarks are only observed in colour neutral bound states. The strong interactions are described using a Yang-Mills theory. These type of theories exhibits asymptotic freedom, i.e. the coupling is weak at high energies. This means that the theory is perturbative at high energies only. Understanding quark confinement requires knowledge of the non perturbative regime. One attempt has been to identify the proper order parameters for describing the low energy limit and then to write down effective actions in terms of these order parameters. We discuss one possible scenario for confinement and the effective models constructed with this as inspiration. Further we discuss solitons in these models and their properties.</p><p>Yang-Mills theory has also become important in the context of string theory. According to the AdS/CFT correspondence string theory in AdS₅×S⁵ is dual to four dimensional Yang-Mills with four supersymmetries. The duality relate the non perturbative regime of one of the theories to the perturbative regime of the other. This makes it in general hard to test this conjecture. For a special type of solutions it is however possible to use a perturbative expansion in both theories. We discuss this type of solutions and in particular we discuss a method, the Bethe ansatz, to find the solutions on the gauge theory side.</p>

One of the still big problems in the Standard Model of particle physics is the problem of confinement. Quarks or other coloured particles have never been observed in isolation. Quarks are only observed in colour neutral bound states. The strong interactions are described using a Yang-Mills theory. These type of theories exhibits asymptotic freedom, i.e. the coupling is weak at high energies. This means that the theory is perturbative at high energies only. Understanding quark confinement requires knowledge of the non perturbative regime. One attempt has been to identify the proper order parameters for describing the low energy limit and then to write down effective actions in terms of these order parameters. We discuss one possible scenario for confinement and the effective models constructed with this as inspiration. Further we discuss solitons in these models and their properties. Yang-Mills theory has also become important in the context of string theory. According to the AdS/CFT correspondence string theory in AdS5×S5 is dual to four dimensional Yang-Mills with four supersymmetries. The duality relate the non perturbative regime of one of the theories to the perturbative regime of the other. This makes it in general hard to test this conjecture. For a special type of solutions it is however possible to use a perturbative expansion in both theories. We discuss this type of solutions and in particular we discuss a method, the Bethe ansatz, to find the solutions on the gauge theory side.

O objetivo principal desta dissertação é estudar a ressonância $\\k$, um méson escalar ainda hoje bastante controverso na comunidade científica. Estudamos o espalhamento elástico $K\\pi$, pois é neste subsistema que o $\\k$ se manifesta como um estado intermediário. A partir de uma lagrangiana efetiva quiral $SU(3)\\times SU(3)$, envolvendo termos de contato e ressonâncias, calculamos a amplitude $K\\pi$ projetada no canal de isospin $1/2$ e em seguida a unitarizamos por meio de {\\it loops} mesônicos. Investigamos os pólos físicos da amplitude, dados pelos zeros do seu denominador que se encontram na segunda superfície de Riemann. Esses zeros podem ser obtidos numericamente, mas a análise estrita desta solução não fornece informações a respeito da dinâmica que produz os pólos. Como alternativa, uma descrição qualitativa dos pólos foi obtida considerando o limite de $SU(2) \\Leftrightarrow M_\\p=0$ e a aproximação da matriz K, que corresponde a unitarizar a amplitude com {\\it loops} de $K\\p$ na camada de massa. Essas simplificações reduzem o denominador da amplitude a um polinômio de segundo grau, que dá origem a dois pólos físicos, posteriormente identificados como sendo o $K^*_0(1430)$ e o $\\k$. Este modelo simplificado permite uma boa interpretação da origem dinâmica dos pólos. O $\\k$ mostrou-se estável na variação dos acoplamentos da ressonância explícita, o que indica que ele é produzido pelo diagrama de contato. Já a ressonância identificada como o $K^*_0(1430)$ varia de um estado ligado a um pólo não físico, dependendo dos valores atribuídos aos parâmetros da ressonância, o que sugere fortemente que a natureza destes pólos é distinta. Esses diferentes comportamentos dinâmicos também foram observados no programa numérico, indicando que a essência dos pólos foi mantida no modelo simplificado. % Com o programa numérico obtivemos a posição do pólo do $\\k$ em $(0.7505 \\pm 0.0010) - i\\, (0.2363 \\pm 0.0023)\\;$GeV, o que está em pleno acordo com diversos modelos quirais muito mais complicados. / This work aims mostly at studying the $\\k$ resonance, which is still a controversial scalar meson nowadays within the scientific community. We studied the $K\\pi$ elastic scattering, because the $\\k$ appears as an intermediate state in this subsystem. From an effective chiral lagrangian $SU(3)\\times SU(3)$, involving contact terms and resonances, we calculated the $K\\pi$ amplitude projected on the $1/2$ isospin channel and then unitarized by means of mesonic {\\it loops}. The physical poles of the amplitude were investigated, given by the zeros of its denominator which are encountered on the Riemanns surface. Although these zeros can be numerically obtained, the strict analysis of this solution does not supply information about the poles producing dynamics. Alternatively, a qualitative description of the poles was obtained considering the $SU(2) \\Leftrightarrow M_\\p=0$ limit and the K matrix approximation, which corresponds to the unitarizing of the amplitude with {\\it loops} of $K\\p$ on shell. These simplifications reduce the amplitude denominator to a second grade polynomial that originates two physical poles, later identified as being $K^*_0(1430)$ and $\\k$. This simplified model allows for a good interpretation of the poles dynamic origin. The $\\k$ has been stable on the explicit resonance coupling, showing that it is produced by the contact diagram. The $K^*_0(1430)$ identified resonance, on the other hand, varies from a bounded state to a non-physical pole, depending on the resonance parameters attributed values, which strongly suggest that the nature of this poles is distinct. These different dynamic behaviors have also been observed in the numerical programs, indicating that the essence of the poles was maintained in the simplified model. With the numerical programs we obtained the position of pole $\\k$ in $(0.7505 \\pm 0.0010) - i\\, (0.2363 \\pm 0.0023)\\;$GeV, which is in accordance with various more complex chiral models.

Les travaux présentés dans ce manuscrit sont consacrés à l'étude des molécules d'éthylène C2H4 et de méthane CH4 pour des applications planétologiques et astrophysiques. La première partie de ce travail de thèse concerne la construction de surfaces ab initio (surface d'énergie potentielle et surfaces de moment dipolaire) pour l'éthylène. Une procédure permettant la détermination précise de la géométrie d'équilibre de cette molécule a été mise en place, car elle conditionne en partie la précision sur les niveaux rotationnels. Dans la seconde partie, ces surfaces ont été utilisés pour le calcul des niveaux d'énergie vibrationnels de l'éthylène et des isotopologues 12C2D4, 13C2H4 et 13C12CH4 par calcul variationnel, ainsi que l'étude des positions et intensités de raies pour les molécules 12C2H4 et 13C12CH4. Ces nouvelles surfaces ont permis des avancées significatives pour la prédiction variationnelle ab initio des spectres de l'éthylène. L'extension de ces calculs à l'étude de ces spectres à des températures élevées, pour des applications astrophysiques, a été pour la première fois abordée. La dernière partie concerne la construction non empirique d'un modèle effectif pour le moment dipolaire du méthane à partir de surfaces ab initio. Pour cela, une technique algébrique, basée sur la méthode des Transformations de Contact, et développée au sein de notre équipe pour les molécules triatomiques, a été pour la première fois étendue au cas des molécules penta-atomiques. L'ensemble de ces résultats a été confronté aux informations présentes dans les bases de données spectroscopiques, ce qui a permis de valider nos différentes approches. / The work presented in this manuscript is devoted to the study of ethyleneC2H4 and methane CH4 for planetological and astrophysical applications. The first part of this thesis concerns the construction of ab initio surfaces (potential energy surface and dipole moment surfaces ) for ethylene molecule. A procedure for the accurate determination of the equilibrium geometry in this molecule has been established, because it determines partially the accuracy of the rotational levels. In the second part, these surfaces were used to calculate the vibrational energy levels of ethylene and isotopologues 12C2D4, 13C2H4 and 13C12CH4 by variational calculations, and the study of the line positions and line intensities for 12C2H4 and 13C12CH4 molecules. These new surfaces have led to significant advances in ab initio variational predictions of ethylene spectra. For the first time, the extension of these calculations to the study of spectra at high-temperatures, for astrophysicalapplications were addressed. The last part concerns the non-empirical constructionof effective models for the dipole moment of methane from ab initio surfaces. For thisstudy, an algebraic technique based on the Contact Transformations approach, and developed in our team for triatomic molecules has been extended to the case of penta-atomic molecules for the very first time. All of these results was confronted with informations in spectroscopic databases, which were used to validate our approaches.