Este trabalho aborda a formulação geométrica das teorias clássicas de calibre, ou Yang-Mills, considerando-as como uma importante classe de modelos que deve ser incluída em qualquer tentativa de estabelecer um formalismo matemático geral para a teoria clássica dos campos. Tal formulação deve vir em (pelo menos) duas variantes: a versão hamiltoniana, que passou por uma fase de desenvolvimento rápido durante os últimos 10-15 anos, levando ao que hoje é conhecido como o ``formalismo multissimplético\'\', e a mais tradicional versão lagrangiana utilizada nesta tese. O motivo principal justificando tal investigação é que teorias de calibre constituem os mais importantes exemplos de sistemas dinâmicos que são altamente relevantes na Física e onde a equivalência entre a versão lagrangiana e a versão hamiltoniana, que no caso de sistemas não-singulares é estabelecida pela transformação de Legendre, deixa de ser óbvia, pois teorias de calibre são sistemas degenerados do ponto de vista lagrangiano e são sistemas vinculados do ponto de vista hamiltoniano. Esta propriedade característica das teorias de calibre é uma consequência direta do seu alto grau de simetria, isto é, da sua invariância de calibre. No entanto, numa formulação plenamente geométrica da teoria clássica dos campos, capaz de incorporar situações topologicamente não-triviais, a invariância sob transformações de calibre locais (transformações de calibre de segunda espécie) e, surpreendentemente, até mesmo a invariância sob as transformações de simetria globais correspondentes (transformações de calibre de primeira espécie) não podem ser adequadamente descritas em termos de grupos de Lie e suas ações em variedades, mas requerem a introdução e o uso sistemático de um novo conceito, a saber, fibrados de grupos de Lie e suas ações em fibrados (sobre a mesma variedade base). A meta principal da presente tese é tomar os primeiros passos no desenvolvimento de ferramentas matemáticas adequadas para lidar com este novo conceito de simetria e, como uma primeira aplicação, dar uma definição clara e simples do procedimento de ``acoplamento mínimo\'\' e uma demonstração simples do teorema de Utiyama, segundo o qual lagrangianas para potenciais de calibre (conexões) de primeira ordem (i.e., que dependem apenas dos próprios potenciais de calibre e de suas derivadas parciais até primeira ordem) que são invariantes sob transformações de calibre são necessariamente funções dos campos de calibre (i.e., do tensor de curvatura) invariantes sob as transformações de simetria globais correspondentes. / This thesis deals with the geometric formulation of classical gauge theories, or Yang-Mills theories, regarded as an important class of models that must be included in any attempt to establish a general mathematical framework for classical field theory. Such a formulation must come in (at least) two variants: the hamiltonian version which has gone through a phase of rapid development during the last 10-15 years, leading to what is now known as the ``multisymplectic formalism\'\', and the more traditional lagrangian version studied in this thesis. The main motivation justifying this kind of investigation is that gauge theories constitute the most important examples of dynamical systems that are highly relevant in physics and where the equivalence between the lagrangian and the hamiltonian version, which for non-singular systems is established through the Legendre trans% formation, is far from obvious, since gauge theories are degenerate systems from the lagrangian point of view and are constrained systems from the hamiltonian point of view. This characteristic property of gauge theories is a direct consequence of their high degree of symmetry, that is, of gauge invariance. However, in a fully geometric formulation of classical field theory, capable of incorporating topologically non-trivial situations, invariance under local gauge transformations (gauge transformations of the second kind) and, surprisingly, even invariance under the corresponding global symmetry transformations (gauge transformations of the first kind) cannot be described adequately in terms of Lie groups and their actions on manifolds but requires the introduction and systematic use of a new concept, namely Lie group bundles and their actions on fiber bundles (over the same base manifold). The main goal of the present thesis is to take the first steps in developing adequate mathematical tools for handling this new concept of symmetry and, as a first application, give a simple clear-cut definition for the prescription of ``minimal coupling\'\' and a simple proof of Utiyama´s theorem, according to which lagrangians for gauge potentials (connections) that are gauge invariant and of first order, i.e., dependent only on the gauge potentials themselves and on their partial derivatives up to first order, are necessarily functions of the gauge field strengths (i.e., the curvature tensor) invariant under the corresponding global symmetry transformations.

Com os próximos grandes projetos the observação do Universo, a cosmologia entrará em uma era de alta precisão de medidas. Novos dados trarão um novo entendimento da evolução do Universo, seus principais componentes e do comportamento da gravi- dade. Sendo assim, é fundamental também ter uma boa predição teórica para a formação de estrutura de larga escala em regime não-linear. A melhor maneira de resolver as equações hidrodinâmicas que descrevem o nosso universo é por meio de simulações cosmológicas na rede. Entretando, estas contém desafios, como a correta inclusão de física bariônica e a diminuição do alto tempo computacional. Uma outra abordagem muito usada é o cálculo das funções de cor- relação por meio de métodos perturbativos (em inglês, Standard Perturbation Theory, ou SPT). Entretanto, esta contém problemas variados: pode não convergir para algu- mas cosmologias e, caso convirja, não há certeza de convergência para o resultado correto. Além disso, há uma escala privilegiada nos limites integrais que envolvem o método perturbativo. Nós calculamos o resultado por esse método até terceira ordem e mostramos que o termo de terceira ordem é ainda maior que o de 2-loops e 3-loops. Isso evidencia alguns problemas descritos com o método perturbativo. O método de Teorias Efetivas de Campo aplicado ao estudo de LSS busca corrigir os problemas da SPT e, desta forma, complementar os resultados de simulações na rede. Em outras áreas da física, como a Cromodinâmica Quântica de baixas energias, EFTs também são usadas como um complemento a essas simulações na rede. EFTs melhoram a predição do espectro de potência da matéria por meio da inclusão dos chamados contra-termos, que precisam ser fitados em simulações. Estes contratermos, que são parâmetros livres, contém importante informação sobre como a física em pequenas escalas afeta a física nas escalas de interesse. Explicaremos os resultados para a predição em 3-loops de EFT, trabalho inédito. É possível usar as EFTs também no problema de conectar a campo de matéria com outros traçadores, como os halos e as galáxias, chamado de bias. Com as EFTs podemos construir uma base completa de operadores para parametrizar o bias. Será explicado como utilizar esses operadores para melhorar a predição do bias em escalas não-lineares. Serão calculados esses termos de EFT em simulações. Também será mostrado como renormalizar o bias em coordenadas de Lagrange. Por fim, será explicada outra importante aplicação das EFTs em cosmologia, mais especificamente em teorias de inflação. EFTs parametrizam desvios nas teorias de um campo único no chamado regime de slow-roll. / With future cosmological surveys, cosmology will enter in the precision era. New data will improve the constraints on the standard cosmological model enhancing our knowledge about the universe history, its components and the behavior of gravity. In this context, it is vital to come up with precise theoretical predictions for the formation of large-scale structure beyond the linear regime. The best way of solving the fluid equations that describe the large-scale universe is through lattice simulations, which faces difficulties in the inclusion of accurate baryonic physics and is very computationally costly. Another approach is the theoreti- cal calculation of the correlation statistics through the perturbative approach, called Standard Perturbation Theory (SPT). However, SPT has several problems: for some cosmologies, it may not converge and even when it converges, we cannot be sure it converges to the right result. Also, it contains a special scale that is the loop momenta upper-bound in the integral. In this work, we show results for the 3-loop calculation. The term of third order is larger than the terms of 2-loops and 3-loops, making explicit SPT problems. In this work, we describe the recent usage of Effective Field Theories (EFTs) on Large Scale Structure problems to correct SPT issues and complement cosmological simulations. EFTs are used in other areas of physics, such as low energy QCD, serving as a complement to lattice calculations. EFT improves the predictions for the matter power spectrum and bispectrum by adding counterterms that need to be fitted. The free parameters, instead of being a problem, bring relevant information about how the small-scale physics affects the scales for which we are trying to make statistical predictions. We show the calculation of the 3-loop EFT counterterms. EFTs are also used to explain main points connecting the matter density field with tracers like galaxies and halos. EFTs highlighted how to construct a complete basis of operators that parametrize the bias. We explain how we can use EFT to improve the bias prediction to non-linear scales. We compute the non-linear halo-bias by fitting the bias parameters in simulations. We also show the EFT renormalization in Lagrangian coordinates. Finally, we explain another critical EFT application to cosmology: in primordial physics. It can be used to parametrize deviations to the slow-roll theory within the inflationary paradigm.

Which tensor fields G on a smooth manifold M can serve as a spacetime structure? In the first part of this thesis, it is found that only a severely restricted class of tensor fields can provide classical spacetime geometries, namely those that can carry predictive, interpretable and quantizable matter dynamics. The obvious dependence of this characterization of admissible tensorial spacetime geometries on specific matter is not a weakness, but rather presents an insight: it was Maxwell theory that justified Einstein to promote Lorentzian manifolds to the status of a spacetime geometry. Any matter that does not mimick the structure of Maxwell theory, will force us to choose another geometry on which the matter dynamics of interest are predictive, interpretable and quantizable. These three physical conditions on matter impose three corresponding algebraic conditions on the totally symmetric contravariant coefficient tensor field P that determines the principal symbol of the matter field equations in terms of the geometric tensor G: the tensor field P must be hyperbolic, time-orientable and energy-distinguishing. Remarkably, these physically necessary conditions on the geometry are mathematically already sufficient to realize all kinematical constructions familiar from Lorentzian geometry, for precisely the same structural reasons. This we were able to show employing a subtle interplay of convex analysis, the theory of partial differential equations and real algebraic geometry. In the second part of this thesis, we then explore general properties of any hyperbolic, time-orientable and energy-distinguishing tensorial geometry. Physically most important are the construction of freely falling non-rotating laboratories, the appearance of admissible modified dispersion relations to particular observers, and the identification of a mechanism that explains why massive particles that are faster than some massless particles can radiate off energy until they are slower than all massless particles in any hyperbolic, time-orientable and energy-distinguishing geometry. In the third part of the thesis, we explore how tensorial spacetime geometries fare when one wants to quantize particles and fields on them. This study is motivated, in part, in order to provide the tools to calculate the rate at which superluminal particles radiate off energy to become infraluminal, as explained above. Remarkably, it is again the three geometric conditions of hyperbolicity, time-orientability and energy-distinguishability that allow the quantization of general linear electrodynamics on an area metric spacetime and the quantization of massive point particles obeying any admissible dispersion relation. We explore the issue of field equations of all possible derivative order in rather systematic fashion, and prove a practically most useful theorem that determines Dirac algebras allowing the reduction of derivative orders. The final part of the thesis presents the sketch of a truly remarkable result that was obtained building on the work of the present thesis. Particularly based on the subtle duality maps between momenta and velocities in general tensorial spacetimes, it could be shown that gravitational dynamics for hyperbolic, time-orientable and energy distinguishable geometries need not be postulated, but the formidable physical problem of their construction can be reduced to a mere mathematical task: the solution of a system of homogeneous linear partial differential equations. This far-reaching physical result on modified gravity theories is a direct, but difficult to derive, outcome of the findings in the present thesis. Throughout the thesis, the abstract theory is illustrated through instructive examples. / Welche Tensorfelder G auf einer glatten Mannigfaltigkeit M können eine Raumzeit-Geometrie beschreiben? Im ersten Teil dieser Dissertation wird es gezeigt, dass nur stark eingeschränkte Klassen von Tensorfeldern eine Raumzeit-Geometrie darstellen können, nämlich Tensorfelder, die eine prädiktive, interpretierbare und quantisierbare Dynamik für Materiefelder ermöglichen. Die offensichtliche Abhängigkeit dieser Charakterisierung erlaubter tensorieller Raumzeiten von einer spezifischen Materiefelder-Dynamik ist keine Schwäche der Theorie, sondern ist letztlich genau das Prinzip, das die üblicherweise betrachteten Lorentzschen Mannigfaltigkeiten auszeichnet: diese stellen die metrische Geometrie dar, welche die Maxwellsche Elektrodynamik prädiktiv, interpretierbar und quantisierbar macht. Materiefeld-Dynamiken, welche die kausale Struktur von Maxwell-Elektrodynamik nicht respektieren, zwingen uns, eine andere Geometrie auszuwählen, auf der die Materiefelder-Dynamik aber immer noch prädiktiv, interpretierbar und quantisierbar sein muss. Diesen drei Voraussetzungen an die Materie entsprechen drei algebraische Voraussetzungen an das total symmetrische kontravariante Tensorfeld P, welches das Prinzipalpolynom der Materiefeldgleichungen (ausgedrückt durch das grundlegende Tensorfeld G) bestimmt: das Tensorfeld P muss hyperbolisch, zeitorientierbar und energie-differenzierend sein. Diese drei notwendigen Bedingungen an die Geometrie genügen, um alle aus der Lorentzschen Geometrie bekannten kinematischen Konstruktionen zu realisieren. Dies zeigen wir im ersten Teil der vorliegenden Arbeit unter Verwendung eines teilweise recht subtilen Wechselspiels zwischen konvexer Analysis, der Theorie partieller Differentialgleichungen und reeller algebraischer Geometrie. Im zweiten Teil dieser Dissertation erforschen wir allgemeine Eigenschaften aller solcher hyperbolischen, zeit-orientierbaren und energie-differenzierenden Geometrien. Physikalisch wichtig sind der Aufbau von frei fallenden und nicht rotierenden Laboratorien, das Auftreten modifizierter Energie-Impuls-Beziehungen und die Identifizierung eines Mechanismus, der erklärt, warum massive Teilchen, die sich schneller als einige masselosse Teilchen bewegen, Energie abstrahlen können, aber nur bis sie sich langsamer als alle masselossen Teilchen bewegen. Im dritten Teil der Dissertation ergründen wir die Quantisierung von Teilchen und Feldern auf tensoriellen Raumzeit-Geometrien, die die obigen physikalischen Bedingungen erfüllen. Eine wichtige Motivation dieser Untersuchung ist es, Techniken zur Berechnung der Zerfallsrate von Teilchen zu berechnen, die sich schneller als langsame masselose Teilchen bewegen. Wir finden, dass es wiederum die drei zuvor im klassischen Kontext identifizierten Voraussetzungen (der Hyperbolizität, Zeit-Orientierbarkeit und Energie-Differenzierbarkeit) sind, welche die Quantisierung allgemeiner linearer Elektrodynamik auf einer flächenmetrischen Raumzeit und die Quantizierung massiver Teilchen, die eine physikalische Energie-Impuls-Beziehung respektieren, erlauben. Wir erkunden auch systematisch, wie man Feldgleichungen aller Ableitungsordnungen generieren kann und beweisen einen Satz, der verallgemeinerte Dirac-Algebren bestimmt und die damit Reduzierung des Ableitungsgrades einer physikalischen Materiefeldgleichung ermöglicht. Der letzte Teil der vorliegenden Schrift skizziert ein bemerkenswertes Ergebnis, das mit den in dieser Dissertation dargestellten Techniken erzielt wurde. Insbesondere aufgrund der hier identifizierten dualen Abbildungen zwischen Teilchenimpulsen und -geschwindigkeiten auf allgemeinen tensoriellen Raumzeiten war es möglich zu zeigen, dass man die Gravitationsdynamik für hyperbolische, zeit-orientierbare und energie-differenzierende Geometrien nicht postulieren muss, sondern dass sich das Problem ihrer Konstruktion auf eine rein mathematische Aufgabe reduziert: die Lösung eines homogenen linearen Differentialgleichungssystems. Dieses weitreichende Ergebnis über modifizierte Gravitationstheorien ist eine direkte (aber schwer herzuleitende) Folgerung der Forschungsergebnisse dieser Dissertation. Die abstrakte Theorie dieser Doktorarbeit wird durch mehrere instruktive Beispiele illustriert.

In this thesis, conformal transformations in d and two dimensions and the results of conformal symmetry in classical and quantum field theories are reviewed. After investigating the conformal group and its algebra, various aspects of conformal invariance in field theories, like conserved charges, correlation functions and the Ward identities are discussed. The central charge and the Virasoro algebra are briefly touched upon.

Gauge theories are one of the corner stones of modern theoretical physics. They describe the nature of all fundamental interactions and have been applied in multiple branches of physics. The most challenging problem of gauge theories, which has not been solved yet, is their strong coupling dynamics. A class of gauge theories that admits simplifications allowing to deal with the strong coupling regime are supersymmetric ones. For example, recently proposed method of supersymmetric localization allows to reduce expectation values of supersymmetric observables, expressed through the path integral, to finite-dimensional matrix integral. The last one is usually easier to deal with compared to the original infinite-dimensional integral. This thesis deals with the matrix models obtained from the localization of different 5D gauge theories. The focus of our study is N=1 super Yang-Mills theory with different matter content as well as N=1 Chern-Simons-Matter theory with adjoint hypermultiplets. Both theories are considered on the five-spheres. We make use of the saddle-point approximation of the matrix integrals, obtained from localization, to evaluate expectation values of different observables in these theories. This approximation corresponds to the large-N limit of the localized gauge theory. We derive <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?N%5E%7B3%7D" /> behavior for the free energy of 5D N=1* super Yang-Mills theory at strong coupling. This result is important in light of the relation between 5D theory and the world-volume theories of M5-branes, playing a significant role in string theory. We have also explored rich phase structure of 5D SU(N) N=1 super Yang-Mills theory coupled to massive matter in different representations of the gauge group. We have shown that in the case of the massive adjoint hypermultiplet theory undergoes infinite chain of the third order phase transitions while interpolating between weak and strong coupling in the decompactification limit. Finally, we obtain several interesting results for 5D Chern-Simons theory, suggesting existence of the holographic duals to this theory. In particular, we derive <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?N%5E%7B5/2%7D" /> behavior of the free energy of this theory, which reproduces the behavior of the free energy for 5D theories with known  holographic duals.

In this thesis we study the connection between continuum quantum field theory and corresponding lattice field theory, specifically for two cases: Landau gauge fixing and ’t Hooft-Polyakov monopoles. To study non-perturbative phenomena such as the confinement mechanism of quarks and gluons and dynamical chiral symmetry breaking in Quantum Chromodynamics (QCD), there are two major approaches: the Dyson-Schwinger equations (DSEs) approach, which is based on the covariant continuum formulation, and lattice gauge theory. The strength and beauty of lattice gauge theory is due to the fact that gauge invariance is manifest and fixing a gauge is not required. In the covariant continuum formulation of gauge theories, on the other hand, one has to deal with the redundant degrees of freedom due to gauge invariance and has to fix gauge (most popularly, Landau gauge). There, the gauge-fixing machinery is based on the so-called Faddeev-Popov procedure or more generally, the Becchi-Rouet-Stora-Tyutin (BRST) symmetry. Beyond perturbation theory this is aggravated by the existence of so-called Gribov copies, however, that satisfy the same gauge-fixing condition, but are related by gauge transformations, and are thus physically equivalent. When attempting to fix Landau gauge on the lattice to make a connection with its continuum counterpart, this ambiguity manifests itself in the Neuberger 0/0 problem that asserts that the expectation value of any physical observable will always be of the indefinite form 0/0. We explain the topological nature of this problem and how the complete cancellation of Gribov copies can be avoided in a modified lattice Landau gauge based on a new definition of gauge fields on the lattice as stereographically projected link variables. For compact U(1), where the Gribov copy problem is related to the classification the local minima of XY spin glass models, we explicitly show that there still remain Gribov copies but their number is exponentially reduced in lower dimensional models. We then formulate the corresponding Faddeev-Popov procedure on the lattice, for these models. Moreover, we explicitly demonstrate that the proposed modification circumvents the Neuberger 0/0 problem for lattices of arbitrary dimensions for compact U(1). Applied to the maximal Abelian subgroup this will avoid the perfect cancellation amongst the remaining Gribov copies for SU(N), and so the corresponding BRST formulation is also then possible for generic SU(N), in particular, for the Standard Model groups. For higher dimensional lattices, the gauge fixing conditions for both the standard and the modified lattice Landau gauges are systems of multivariate nonlinear equations, solving which in general is a highly non-trivial task. However, we show that these systems can be interpreted as systems of polynomial equations. They can then be solved exactly by computational Algebraic Geometry, the Groebner basis technique in particular, and numerically by the Polynomial Homotopy Continuation method. ’t Hooft-Polyakov monopoles play an important role in high energy physics due to their presence in grand unified theories and their usefulness in studying non-perturbative properties of quantum field theories through electric-magnetic dualities. In the second part of the thesis, we study adjoint Higgs models, which exhibit ’t Hooft-Polyakov monopoles, and have been extensively analyzed using semi-classical analysis in the continuum. However, to study them in a fully nonperturbative fashion, it is essential to put the theory on the lattice. Here, we investigate twisted C-periodic boundary conditions in SU(N) gauge field theory with an adjoint Higgs field and show that for even N with a suitable twist one can impose a non-zero magnetic charge relative to each of N − 1 residual U(1)’s in the broken phase, thereby creating ’t Hooft-Polyakov magnetic monopoles. This makes it possible then to use lattice Monte-Carlo simulations to study the properties of these monopoles in the full quantum theory and compare them with the existing results in the continuum. / Thesis (Ph.D.) -- University of Adelaide, School of Chemistry and Physics, 2010

Thesis (Ph. D.)--University of Notre Dame, 2008. / Thesis directed by Don Howard for the Graduate Program in History and Philosophy of Science. "April 2008." Includes bibliographical references (leaves 212-220).

Název práce: Studium efektivních Lagrangianů a jejich aplikace Autor: Jaroslav Trnka Katedra: Ústav částicové a jaderné fyziky Vedoucí disertační práce: RNDr. Jiří Novotný, CSc., ÚČJF Abstrakt: V této práci studujeme různé aspekty efektivních teorií pole pro kvan- tovou chromodynamiku (QCD). V prvních dvou kapitolách se zaměříme na efek- tivní teorii pro resonance, která interpoluje mezi nízkoenergetickou efektivní teorií (Chirální poruchová teorie) a vysokoenergetickou QCD. V rámci této teorie studu- jeme jednosmyčkovou renormalizaci, jak z pohledu výpočetního pomocí SS-PP korelátoru, tak i čistě koncepčního studiem dynamicky generovaných stupňů vol- nosti. Ve čtvrté kapitole studujeme amplitudy rozptylu v rámci nelineárního sig- ma modelu, který představuje vedoucí člen nízkoenergetické efektivní teorie pro QCD. V návaznosti na nedávné objevy v rámci Yang-Mills teorie se nám podaří v rámci tohoto modelu zkonstruovat rekurzivní relace pro stromové amplitudy. Kromě čistě teoretické důležitosti tohoto faktu představuje tato metoda efektivní výpočetní nástroj nezávislý na formulaci amplitud pomocí Feynmanovských dia- gramů. Klíčová slova: efektivní teorie pole, kvantová chromodynamika, nelineární sigma model...

In this thesis, we investigate four dimensional supersymmetric indices. The motivation for studying such objects lies in the physics of Seiberg's electric-magnetic duality in supersymmetric field theories. In the first chapter, we first define the index and underline its cohomological nature, before giving a first computation based on representation theory of free superconformal field theories. After listing all representations of the superconformal algebra based on shortening conditions, we compute the associated Verma module characters, from which we can extract the index in the appropriate limit. This approach only provides us with the free field theory limit for the index and does not account for the values of the $R$-charges away from free field theories. To circumvent this limitation, we then study a theory on $\mathbb{R}\times S^3$ which allows for a computation of the superconformal index for multiplets with non-canonical $R$-charges. We expand the fields in harmonics and canonically quantise the theory to analyse the set of quantum states, identifying the ones that contribute to the index. To go beyond free field theory on $\mathbb{R}\times S^3$, we then use the localisation principle to compute the index exactly in an interacting theory, regardless of the value of the coupling constant. We then show that the index is independent of a particular geometric deformation of the underlying manifold, by squashing the sphere. In the final chapter, we show how the matching of the index can be used in the large $N$ limit to identify the $R$-charges for all fields of the electric-magnetic theories of the canonical Seiberg duality. We then conclude by outlining potential further work.

Com os próximos grandes projetos the observação do Universo, a cosmologia entrará em uma era de alta precisão de medidas. Novos dados trarão um novo entendimento da evolução do Universo, seus principais componentes e do comportamento da gravi- dade. Sendo assim, é fundamental também ter uma boa predição teórica para a formação de estrutura de larga escala em regime não-linear. A melhor maneira de resolver as equações hidrodinâmicas que descrevem o nosso universo é por meio de simulações cosmológicas na rede. Entretando, estas contém desafios, como a correta inclusão de física bariônica e a diminuição do alto tempo computacional. Uma outra abordagem muito usada é o cálculo das funções de cor- relação por meio de métodos perturbativos (em inglês, Standard Perturbation Theory, ou SPT). Entretanto, esta contém problemas variados: pode não convergir para algu- mas cosmologias e, caso convirja, não há certeza de convergência para o resultado correto. Além disso, há uma escala privilegiada nos limites integrais que envolvem o método perturbativo. Nós calculamos o resultado por esse método até terceira ordem e mostramos que o termo de terceira ordem é ainda maior que o de 2-loops e 3-loops. Isso evidencia alguns problemas descritos com o método perturbativo. O método de Teorias Efetivas de Campo aplicado ao estudo de LSS busca corrigir os problemas da SPT e, desta forma, complementar os resultados de simulações na rede. Em outras áreas da física, como a Cromodinâmica Quântica de baixas energias, EFTs também são usadas como um complemento a essas simulações na rede. EFTs melhoram a predição do espectro de potência da matéria por meio da inclusão dos chamados contra-termos, que precisam ser fitados em simulações. Estes contratermos, que são parâmetros livres, contém importante informação sobre como a física em pequenas escalas afeta a física nas escalas de interesse. Explicaremos os resultados para a predição em 3-loops de EFT, trabalho inédito. É possível usar as EFTs também no problema de conectar a campo de matéria com outros traçadores, como os halos e as galáxias, chamado de bias. Com as EFTs podemos construir uma base completa de operadores para parametrizar o bias. Será explicado como utilizar esses operadores para melhorar a predição do bias em escalas não-lineares. Serão calculados esses termos de EFT em simulações. Também será mostrado como renormalizar o bias em coordenadas de Lagrange. Por fim, será explicada outra importante aplicação das EFTs em cosmologia, mais especificamente em teorias de inflação. EFTs parametrizam desvios nas teorias de um campo único no chamado regime de slow-roll. / With future cosmological surveys, cosmology will enter in the precision era. New data will improve the constraints on the standard cosmological model enhancing our knowledge about the universe history, its components and the behavior of gravity. In this context, it is vital to come up with precise theoretical predictions for the formation of large-scale structure beyond the linear regime. The best way of solving the fluid equations that describe the large-scale universe is through lattice simulations, which faces difficulties in the inclusion of accurate baryonic physics and is very computationally costly. Another approach is the theoreti- cal calculation of the correlation statistics through the perturbative approach, called Standard Perturbation Theory (SPT). However, SPT has several problems: for some cosmologies, it may not converge and even when it converges, we cannot be sure it converges to the right result. Also, it contains a special scale that is the loop momenta upper-bound in the integral. In this work, we show results for the 3-loop calculation. The term of third order is larger than the terms of 2-loops and 3-loops, making explicit SPT problems. In this work, we describe the recent usage of Effective Field Theories (EFTs) on Large Scale Structure problems to correct SPT issues and complement cosmological simulations. EFTs are used in other areas of physics, such as low energy QCD, serving as a complement to lattice calculations. EFT improves the predictions for the matter power spectrum and bispectrum by adding counterterms that need to be fitted. The free parameters, instead of being a problem, bring relevant information about how the small-scale physics affects the scales for which we are trying to make statistical predictions. We show the calculation of the 3-loop EFT counterterms. EFTs are also used to explain main points connecting the matter density field with tracers like galaxies and halos. EFTs highlighted how to construct a complete basis of operators that parametrize the bias. We explain how we can use EFT to improve the bias prediction to non-linear scales. We compute the non-linear halo-bias by fitting the bias parameters in simulations. We also show the EFT renormalization in Lagrangian coordinates. Finally, we explain another critical EFT application to cosmology: in primordial physics. It can be used to parametrize deviations to the slow-roll theory within the inflationary paradigm.