Submitted by Renata Lopes (renatasil82@gmail.com) on 2016-12-22T13:25:11Z No. of bitstreams: 1 vahidnikoofard.pdf: 794368 bytes, checksum: 26feb8d15d2757f79f8d7dfb69b610c2 (MD5) / Approved for entry into archive by Diamantino Mayra (mayra.diamantino@ufjf.edu.br) on 2017-01-31T10:20:21Z (GMT) No. of bitstreams: 1 vahidnikoofard.pdf: 794368 bytes, checksum: 26feb8d15d2757f79f8d7dfb69b610c2 (MD5) / Made available in DSpace on 2017-01-31T10:20:21Z (GMT). No. of bitstreams: 1 vahidnikoofard.pdf: 794368 bytes, checksum: 26feb8d15d2757f79f8d7dfb69b610c2 (MD5) Previous issue date: 2015-06-30 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Esta tese é composta por assuntos distintos entre si de teorias quânticas de campos onde alguns deles são descritos em espaços não-comutativos (NC). Em primeiro lugar, analisamos a dinâmica de uma partícula livre sobre uma 2-esfera e através da dinâmica das suas equações de movimento, obtivemos as perturbações NCs neste espaço de fase. Este modelo sugere uma origem para o Zitterbewegung do elétron. Depois disso, consideramos umaversãoNCdasegundaleideNewtonparaestemodelo, quefoiobtidocomestecenário geométrico aplicado a este modelo. Em seguida, discutimos um formalismo alternativo relacionado à não-comutatividade chamado DFR onde o parâmetro NC é considerado uma coordenada e demonstramos exatamente que ela tem obrigatoriamente um momento conjugado neste espaço de fase DFR, diferentemente do que alguns autores da atual literatura sobre DFR afirmam. No próximo assunto, usando o formalismo de solda que, em poucaspalavras,colocapartículascomquiralidadesopostasnomesmomultipleto,soldamos algumas versões NCs de modelos bem conhecidos como modelos de Schwinger quirais e modelos (anti) auto duais no espaço-tempo de Minkowski estendido. Em outro assunto estudado aqui, também construímos a versão NC do modelo de Jackiw-Pi com um grupo de calibre arbitrário e usamos o mapeamento bem conhecido de Seiberg-Witten para obter este modelo NC em termos de variáveis comutativos. Finalmente, utilizamos o formalismo de campos e anticampos (ou método BV) para construir a ação de Batalin-Vilkovisky (BV) do modelo Jackiw-Pi estendido e após o prEntendiocedimento de fixação de calibre chegamos a uma ação completa, pronta para quantização. / This thesis is composed of distinct aspects of quantum field theories where some of them are described in noncommutative (NC) spaces. Firstly, we have analyzed the dynamics of a free particle over a 2-sphere and through the dynamics of the equations of motion we have derived its NC perturbations in the phase-space. This model suggests an origin for Zitterbewegung feature of the electron. After that we have considered the NC version of Newton’s second law for this model, which was obtained with the geometricalscenarioappliedtothismodel. Thenwehavediscussedtheso-calledDoplicher– Fredenhagen–Roberts (DFR) alternative formalism concerning noncommutativity where the NC parameter has a coordinate role and we showed exactly that it has a conjugated momentum in the DFR phase-space, differently of what some authors of the current DFR-literature claims. In the next issue, using the soldering formalism which, in few words, put opposite chiral particles in the same multiplet, we have soldered some NC versions of well known models like the chiral Schwinger model and (anti)self dual models in the extended Minkowski spacetime. Changing the subject, we have constructed the NC spacetime version of Jackiw-Pi model with an arbitrary gauge group and we used the well known Seiberg-Witten map to obtain the NC model expressed in terms of commutative variables. Finally, we have used the field-antifield (or BV method) formalism to construct the Batalin-Vilkovisky (BV) action of the extended Jackiw-Pi model and after the gauge fixing procedure we have arrived at a quantized-ready action for this model.

Esta tese trata a existência de Princpios de Grandes Desvios (PGD), no âmbito de sistemas fermiônicos em equilbrio. A motivação fsica detrás de nossos estudos são medidas experimentais de resistência elétrica de nanofios de silcio dopados com átomos de fósforo. Estas medidas mostram que efeitos quânticos no transporte de carga elétrica quase desaparecem para nanofios de comprimentos maiores que alguns nanômetros, mesmo para temperaturas muito baixas (4.2°K). A fim de provar matematicamente tal efeito, dividimos nosso trabalho em diversos passos: 1. No primeiro passo, para férmions não interagentes numa rede com desordem, mostramos que a incerteza quântica da densidade da corrente elétrica microscópica, em torno de seus valores macroscópicos(clássicos), é suprimida exponencialmente rápido em relação ao volume da região da rede onde um campo elétrico externo é aplicado. A desordem é modelada como um potencial elétrico aleatório juntamente com amplitudes aleatórias de saltos com valores complexos. O célebre modelo de Anderson de tight-binding é um exemplo particular do caso geral considerado aqui. Nossa análise matemática é baseada em estimativas de Combes-Thomas, o Teorema Ergódico de Akcoglu-Krengel e no formalismo de Grandes Desvios, em particular o Teorema de Gärtner-Ellis. 2. Em segundo lugar, provamos que, para férmions interagindo fracamente na rede, as funções geradoras J(s), s R de cumulantes de distribuições de probabilidades associadas com estados KMS pode ser escrito como o limite de logartmos de integrais gaussianas de Berezin. Mostramos que os determinantes das covariáncias associadas às integrais gaussianas são majorados uniformemente (via desigualdades de Hölder para normas Schatten). Tais covariâncias são também somáveis, em casos gerais de interesse, incluindo assim, sistemas que não são invariantes por translação. 3. No terceiro passo, analisamos expansões de logartmos de integrais gaussianas de Berezin, e assim combinando com métodos construtivos de teoria quântica de campos, mostramos a analiticidade de J(s) para s nas vizinhanças de 0. Finalmente, discutimos como combinar os passos 2-3, a fim de provar (matematicamente falando) os resultados experimentais mencionados acima para férmions interagindo em equilbrio. De fato, os resultados encontrados nesta tese, generalizam trabalhos prévios no âmbito do PGD usado para o estudo de sistemas quânticos. / This Thesis deals with the existence of Large Deviation Principles (LDP) in the scope of fermionic systems at equilibrium. The physical motivation beyond our studies are experimental measures of electric resistance of nanowires in silicon doped with phosphorus atoms. The latter demonstrate that quantum effects on charge transport almost disappear for nanowires of lengths larger than a few nanometers, even at very low temperature (4.2°K). In order to mathematically prove the latter, we divide our work in several steps: 1. In the first step, for noninteracting lattice fermions with disorder, we show that quantum uncertainty of microscopic electric current density around their (classical) macroscopic values is suppressed, exponentially fast with respect to the volume of the region of the lattice where an external electric field is applied. Disorder is modeled by a random external potential along with random, complex-valued, hopping amplitudes. The celebrated tight-binding Anderson model is one particular example of the general case considered here. Our mathematical analysis is based on Combes-Thomas estimates, the Akcoglu-Krengel ergodic theorem, and the large deviation formalism, in particular the Gärtner-Ellis theorem. 2. Secondly, we prove that for weakly interacting fermions on the lattice, the logarithm moment generating function J(s), s R of probability distributions associated with KMS states can be written as the limit of logarithms of Gaussian Berezin integrals. The covariances of the Gaussian integrals are shown to have a uniform determinant bound (via Hölder inequalities for Schatten norms) and to be summable in general cases of interest, including systems that are not translation invariant. 3. In the third step we analyze expansions of logarithms of Gaussian Berezin integrals, which combined with constructive methods of quantum field theory is useful to show the analyticity of J(s) for s in a neighborhood of 0. We finally discuss how to combine steps 2-3 in order to prove (mathematically speaking) for interacting fermions in equilibrium the experimental results above mentioned. In fact, the found results in this Thesis generalize previous works in the scope of LDP used to study quantum systems.

General ideas in the conformal bootstrap program are covered. Both numerical and analytical approaches to the bootstrap equation are reviewed to show how it can be manipulated in different ways. Further analytical approaches are studied for theories with defects. We consider the three-dimensional CFT at the corresponding WF fixed point in the O(N) \phi^4 model with a co-dimension two, monodromy defect. Anomalous dimensions for bulk- and defect-local fields as well as one of the OPE coefficients are found to the first loop order. Implications of inserting this defect and constraints that arises from symmetries of the theory are investigated.

The Standard Model (SM) of particle physics provides the theoretical framework to describe the fundamental interactions among elementary constituents of matter. SM is supported by experiments to a high degree of accuracy, up to parts per-mil for the electroweak (EW) sector and parts-per-trillion for QED alone, but it still remains incomplete. Many observed phenomena lack explanation in the framework of the SM and its particles. They indicate the possibility of existence of particles and interactions beyond the SM (BSM). These phenomena include dark matter (DM), dark energy and baryonic asymmetry of the universe. In addition, a quantum description of gravity is still lacking. The top quark has the largest mass among the SM particles. Due to it’s heavy mass, top quark is the only colored particle which does not hadronize and hence its properties are directly accessible by studying it’s decay particles. The order one Yukawa coupling of the top quark also imbibes it with an important role in the behavior of the SM couplings at higher energy scales where possible BSM physics may contribute. As a result, precision measurements of top quark properties may provide a glimpse into BSM physics and hence making these measurements is one of the core aims of the Large Hadron Collider. In stark contrast with top quark physics is the elusive, dark matter (DM) of the universe. There exists a lot of observational evidence for it but, as of yet, with no clue with regards to its particle properties and interactions. Compelling evidence for the existence of DM comes from measurements based on cosmic microwave background radiation, astrophysical observations of distribution of visible matter in galaxy clusters, galactic cluster collisions (e.g. bullet cluster), gravitational lensing, galactic rotation curves, structure formation simulations, to name a few. It is interesting to investigate the possibility that there may be a connection between top quark and DM. In this thesis, we extend the SM with simplified models to study BSM physics at colliders and also to explain the DM puzzle. Here, we use the Top quark as a laboratory for constructing generic probes of BSM and also of the dark sector physics. In Chapter 1, we introduce some relevant background and salient aspects of the SM framework on which the following BSM theories are built. In Chapter 2 we explore an s channel and a t-channel simplified model in the context of top quark pair production using asymmetries constructed with kinematic variables of the top decay products. In Chapter 3, we then propose a simplified model which includes a colored scalar as the mediator between DM and SM particles, termed gluphillic scalar dark matter (GSDM). Monojet process is one of the primary channels to probe DM at hadron colliders. In Chapter 3, the discussion of monojet process at the Large Hadron Collider (LHC) is limited to the effective field theory (EFT) framework. In Chapter 4 we discuss collider processes in GSDM model with complete loop calculations for the diagrams involving the mediating colored scalar. We also compare the loop calculation with the EFT results to find the range of applicability of the EFT. The top quark study in Chapter 2 was initially inspired from an interesting observation made in 2008 which suggested a deviation from the SM in the forward-backward asymmetry (FBA) of a pair produced top quark. The value of FBA measured at the time was 18% ±12%. This value deviated by more than 1σ with respect to the SM leading order (LO) value of 5%. The deviation was observed by both the detectors at Tevatron, D0 and CDF, and it’s significance increased with additional data in 2012. Recent analyses of the data by D0 is now in better agreement with the latest effective-NNNLO calculations. However, the FBA measurements by CDF are still in tension with those by D0 and the value predicted by theoretical calculations. Inspired by this puzzle, which may be on its way to getting solved, we have been able to construct effective probes of BSM physics for the on-going and future searches of BSM in the top quark sector. In our analyses, we studied correlations among observables which can distinguish between different sources of BSM contributions in the top quark pair production. As a template, we use an s-channel and a t-channel mediator, both of which leave very different signatures in the kinematic asymmetry correlations. The simplified models considered by us also included parity breaking interactions which lead to polarized top quarks, providing another probe into the underlying production process. We find that all the kinematic distributions of the decay lepton get influenced by the polarization of the top quark. We show that these correlations can distinguish well between the template models of axigluon and diquark. In general, all of these observables also provide a probe into the polarization of the top quark and therefore any chiral couplings with the mediator. However, the lepton polar angle asymmetry measured in the lab frame is special in that it can not only probe the longitudinal polarization as other observables but is also sensitive to the transverse polarization of the top quark. We also show the effectiveness of the proposed top quark kinematic observables, to distinguish between s and t-channel BSM physics models, in future searches for BSM particles at the run-II LHC. In a large verity of dark matter (DM) models the simplest candidate is the model of a singlet scalar particle. The scalar may couple to the standard model in a number of ways via any of the SM particles. Such models with BSM Yukawa interactions or gauge sector extensions are strongly constrained from both the direct detection and collider precision measurements. The remaining models either predict a very heavy dark matter, completely out of reach of collider searches or introduce an unnaturally weak coupling with the SM particles giving no justifications for the small numbers. An interesting corner of the space of possible DM models which has been under-explored so far includes interactions of DM particles with gluons. Although DM particles cannot themselves be charged or colored, a colored scalar mediator can allow this interaction. One such model arises when we consider the scalar DM in presence of a colored scalar particle, for example the one from t-channel model above. Such colored scalars are generically present in a number of BSM theories including SUSY and GUT. How-ever, without the need for any additional gauge symmetries, the two scalars would interact with each other via the marginal operators. In Chapter 3 we study a SM singlet scalar DM candidate which couples to SM via a colored scalar particle. In the GSDM model, DM and mediator interact via the quartic, marginal operator. DM annihilation cross-section of the order of weak interactions (∼ 0.1pb) is predicted to explain the observed dark matter relic density if arising from thermal production of a WIMP DM candidate of mass ∼ 100 GeV. On investigating the GSDM model, we find that it allows a large annihilation cross-section and is still compatible with direct detection bounds. This is so because the annihilation cross-section to a pair of colored scalars proceeds via a tree-level interaction, whereas the interaction with SM particles proceeds via loop diagrams involving the colored scalars. Our work shows that this model is compatible with the observed relic density of DM when the mediating particle is lighter than DM for a large range of the couplings. For masses of the DM and the mediator less then ∼ 50 GeV, the DM can also be lighter than the mediator where the annihilation then proceeds via loop interactions. This region of parameter space is strongly constrained from the collider physics bounds on a colored scalar particle. These bounds become much weaker in the case where the colored scalar does not couple to quarks and hence cannot decay. The bounds coming from long-lived colored scalars become relevant in those cases and also constrain the light mass window. A colored scalar interacting with quarks must do so without violating the strong flavor constraints. We consider the scalar in the framework of a class of models termed minimally flavor violating (MFV) and also assume that it couples only to the right handed up-sector quarks. Such a particle would couple to the top quark and would be observable at the LHC pair production of the top quark. We find constraints on a color triplet particle in such a case and show the coupling and mass regions allowed. Constraints from the decays to light quarks are interpreted from dijet process searches and limit the mass of a color-triplet scalar above 350 GeV. The primary process for direct search of stable particles produced at a collider is a single jet in association with missing transverse energy (MET). We find that in an effective field theory (EFT) framework, very weak bounds are obtained on the mediating scale. In Chapter 4, we perform complete loop calculations for processes involving colored scalar particles and DM at LHC in order to explore the GSDM model at LHC and FCC (Future Circular Collider). The EFT is valid only for mediator masses much heavier than the momentum transfer or the MET cuts. We show the region of applicability of the EFT by comparing it with respect to the loop induced calculation. We analyze the monojet + missing transverse energy (MET) process to find the expected bounds from LHC 13 TeV run-II. We calculate the reach of the LHC in the high luminosity run in the future and also the reach of the FCC to explore the GSDM model. We perform all our calculations for a number of representations of the colored mediator from a triplet to dimension 15. As expected, collider constraints are only significant when the dark matter is light enough (mDM ∼ 10 GeV) to be copiously produced at the LHC. We find that in the high luminosity run, LHC can probe the scalar triplet particle up-to 50 GeV mass in the monojet process though a dimension 15 particle can be probed up to 150 GeV. With an order of magnitude higher beam energy, FCC can rule out much larger parameter space or provide observational evidence for TeV scale mediating particles. In conclusion, this thesis adds to the growing body of literature which points towards BSM discoveries around the corner at high luminosity LHC in the top physics and in dark sector physics. We have also proposed avenues for precision BSM studies at the next generation colliders.

Fedosov has described a geometro-algebraic method to construct in a canonical way a deformation of the Poisson algebra associated with a finite-dimensional symplectic manifold (\\\"phase space\\\"). His algorithm gives a non-commutative, but associative, product (a so-called \\\"star-product\\\") between smooth phase space functions parameterized by Planck\\\''s constant ℏ, which is treated as a deformation parameter. In the limit as ℏ goes to zero, the star product commutator goes to ℏ times the Poisson bracket, so in this sense his method provides a quantization of the algebra of classical observables. In this work, we develop a generalization of Fedosov\\\''s method which applies to the infinite-dimensional symplectic \\\"manifolds\\\" that occur in Lagrangian field theories. We show that the procedure remains mathematically well-defined, and we explain the relationship of this method to more standard perturbative quantization schemes in quantum field theory.

In this project a theoretical study of the so called gyromagnetic ratio was done by investigating classical mechanics, Dirac theory and string theory. The gyromagnetic ratio is a constant term appearing in the coupling between angular momentum and magnetic moment for a particle. A universality in quantum field theory claiming g = 2 regardless of spin is known to exist which also agrees with the found values (g = 2) of the Dirac and string theory. The proof of the aforementioned universality in quantum field theory was sketched in the project by showing that the W-boson Lagrangian is well behaved in the massless limit. Furthermore it is shown that the spin equations of motion for a particle is greatly reduced if g = 2 regardless of spin. / I det här projektet utfördes en teoretisk studie av den så kallade gyromagnetsika kvoten genom att undersöka klassisk mekanik, Dirac-teori och strängteori. Den gyromagnetiska kvoten är en konstant term som visar sig i kopplingen mellan rörelsemängsmoment och magnetiskt moment för en partikel. I kvantfältsteori existerar en universalitet som hävdar att g = 2 oberoende av spin. Denna universalitet stämmer överens med de funna värden på g från Dirac-teori och strängtoeri. Beviset för denna universalitet testades genom ett exempel där Lagrangianen för W-bosonen i kvantfältsteori visades bete sig som förväntat när massan för partikeln tilläts gå mot noll. Vidare undersöktes rörelseekvationerna för ett system helt bestämt av dess spin. I dessa kan det visas att ett universellt värde på g oavsett spin reducerar dessa ekvationer avsevärt.

The time coordinate is a common obstacle in the theory of non-commutative (nc.) spacetimes. Despite that, this work shows how the interplay between quantum fields and an underlying nc. spacetime can still be analyzed, even for the case of nc. time. This is done for the example of a general Moyal-type external potential scattering of the Dirac field in Moyal-Minkowski spacetime. The spacetime is a rare example of a Lorentzian non-compact nc. geometry. Elements of the associated spectral function algebra are shown to be operationally involved at the level of quantum field operators by Bogoliubovs formula. Furthermore, a similar task is attacked in the case of locally nc. spacetimes. An explicit star-product is constructed by a method of Kontsevich. It implements a decay of non-commutativity with increasing distance. This behavior should benefit the technical side - diverse interesting formal attempts are discussed. It is striven for unification of several toy models of nc. spacetimes and a general strategy to define quantum field operators. Within the latter one has to implement the usual quantum behavior as well as a new kind of spacetime behavior. It is shown how this two-fold character causes key difficulties in understanding.

<p>Holographic duality as a rigorous approach to quantum gravity claims that a quantum gravitational system is exactly equal to a quantum theory without gravity in lower spacetime dimensions living on the boundary of the quantum gravitational system. The duality maps key questions about the emergence of spacetime to questions on the non-gravitational boundary system that are accessible to us theoretically and experimentally. Recently, various aspects of quantum information theory on the boundary theory have been found to be dual to the geometric aspects of the bulk theory. In this thesis, we study the exact and approximate quantum error corrections (QEC) in a general quantum system (von Neumann algebras) focused on QFT and gravity. Moreover, we study entanglement theory in the presence of conserved charges in QFT and the multiparameter multistate generalization of quantum relative entropy.</p>

Thema dieser Dissertation ist die Renormierung von perturbativer skalarer Quantenfeldtheorie bei großer Schleifenzahl. Der Hauptteil der Arbeit ist dem Einfluss von Renormierungsbedingungen auf renormierte Greenfunktionen gewidmet. Zunächst studieren wir Dyson-Schwinger-Gleichungen und die Renormierungsgruppe, inklusive der Gegenterme in dimensionaler Regularisierung. Anhand zahlreicher Beispiele illustrieren wir die verschiedenen Größen. Alsdann diskutieren wir, welche Freiheitsgrade ein Renormierungsschema hat und wie diese mit den Gegentermen und den renormierten Greenfunktionen zusammenhängen. Für ungekoppelte Dyson-Schwinger-Gleichungen stellen wir fest, dass alle Renormierungsschemata bis auf eine Verschiebung des Renormierungspunktes äquivalent sind. Die Verschiebung zwischen kinematischer Renormierung und Minimaler Subtraktion ist eine Funktion der Kopplung und des Regularisierungsparameters. Wir leiten eine neuartige Formel für den Fall einer linearen Dyson-Schwinger Gleichung vom Propagatortyp her, um die Verschiebung direkt aus der Mellintransformation des Integrationskerns zu berechnen. Schließlich berechnen wir obige Verschiebung störungstheoretisch für drei beispielhafte nichtlineare Dyson-Schwinger-Gleichungen und untersuchen das asymptotische Verhalten der Reihenkoeffizienten. Ein zweites Thema der vorliegenden Arbeit sind Diffeomorphismen der Feldvariable in einer Quantenfeldtheorie. Wir präsentieren eine Störungstheorie des Diffeomorphismusfeldes im Impulsraum und verifizieren, dass der Diffeomorphismus keinen Einfluss auf messbare Größen hat. Weiterhin untersuchen wir die Divergenzen des Diffeomorphismusfeldes und stellen fest, dass die Divergenzen Wardidentitäten erfüllen, die die Abwesenheit dieser Terme von der S-Matrix ausdrücken. Trotz der Wardidentitäten bleiben unendlich viele Divergenzen unbestimmt. Den Abschluss bildet ein Kommentar über die numerische Quadratur von Periodenintegralen. / This thesis concerns the renormalization of perturbative quantum field theory. More precisely, we examine scalar quantum fields at high loop order. The bulk of the thesis is devoted to the influence of renormalization conditions on the renormalized Green functions. Firstly, we perform a detailed review of Dyson-Schwinger equations and the renormalization group, including the counterterms in dimensional regularization. Using numerous examples, we illustrate how the various quantities are computable in a concrete case and which relations they satisfy. Secondly, we discuss which degrees of freedom are present in a renormalization scheme, and how they are related to counterterms and renormalized Green functions. We establish that, in the case of an un-coupled Dyson-Schwinger equation, all renormalization schemes are equivalent up to a shift in the renormalization point. The shift between kinematic renormalization and Minimal Subtraction is a function of the coupling and the regularization parameter. We derive a novel formula for the case of a linear propagator-type Dyson-Schwinger equation to compute the shift directly from the Mellin transform of the kernel. Thirdly, we compute the shift perturbatively for three examples of non-linear Dyson-Schwinger equations and examine the asymptotic growth of series coefficients. A second, smaller topic of the present thesis are diffeomorphisms of the field variable in a quantum field theory. We present the perturbation theory of the diffeomorphism field in momentum space and find that the diffeomorphism has no influence on measurable quantities. Moreover, we study the divergences in the diffeomorphism field and establish that they satisfy Ward identities, which ensure their absence from the S-matrix. Nevertheless, the Ward identities leave infinitely many divergences unspecified and the diffeomorphism theory is perturbatively unrenormalizable. Finally, we remark on a third topic, the numerical quadrature of Feynman periods.

In dieser Arbeit wird der Ansatz der Weltlinienquantenfeldtheorie (WQFT) zur Berechnung von Observablen des klassischen allgemeinen relativistischen Zweikörpersystems vorgestellt. Kompakte Körper wie Schwarze Löcher oder Neutronensterne werden im Rahmen einer effektiven Feldtheorie mit Weltlinienfeldern beschrieben. Die WQFT behandelt alle Weltlinienfelder gleichberechtigt mit dem Gravitationsfeld und ist definiert als die tree-level-Beiträge eines Pfadintegrals auf diesen Feldern. Zuerst wird die effektive feldtheoretische Beschreibung von kompakten Körpern mit Weltlinien und die post-Minkowski'schen Approximation der Streuung dieser Körpern vorgestellt. Die Einbeziehung des Spins wird mit besonderem Augenmerk auf ihre supersymmetrische Beschreibung in Form von antikommutierenden Grassmann-Variablen analysiert. Anschließend wird die WQFT mit einer Diskussion ihrer in-in Schwinger-Keldysh-Formulierung, ihrer Feynman-Regeln und Graphengenerierung sowie ihrer on-shell Einpunktfunktionen vorgestellt. Die Berechnung von Streuobservablen erfordert im Allgemeinen die Auswertung von Multi-Loop-Integralen, und wir analysieren die Zwei-Loop-Integrale, die in der dritten post-Minkowski'schen Ordnung der Weltlinienobservablen auftreten. Schließlich wenden wir uns den Ergebnissen der WQFT zu und beginnen mit der gravitativen Bremsstrahlung bei der Streuung zweier rotierender Körper. Diese Wellenform wird zusammen mit der Strahlungsinformation der Linear- und Drehimpulsflüsse diskutiert. Der gesamte abgestrahlte Drehimpuls führender post-Minkowski'schen Ordnung wird abgeleitet. Wir präsentieren dann die Ergebnisse des konservativen und strahlenden Impulses und des Spin-Kicks bei dritter post-Minkowski'scher Ordnung und quadratischer Ordnung in Spins zusammen mit der Abbildung der ungebundenen Ergebnisse auf einen konservativen (gebundenen) Hamiltonian bei der entsprechenden perturbativen Ordnung. / In this work the worldline quantum field theory (WQFT) approach to computing observables of the classical general relativistic two-body system is presented. Compact bodies such as black holes or neutron stars are described in an effective field theory by worldline fields with spin degrees of freedom efficiently described by anti-commuting Grassmann variables. Novel results of the WQFT include the gravitational bremsstrahlung at second post-Minkowskian order and the impulse and spin kick at third post-Minkowskian order all at quadratic order in spins. Next, the WQFT is presented with a comprehensive discussion of its in-in Schwinger-Keldysh formulation, its Feynman rules and graph generation and its on-shell one-point functions which are directly related to the scattering observables of unbound motion. Here, we present the second post-Minkowskian quadratic-in-spin contributions to its free energy from which the impulse and spin kick may be derived to the corresponding order. The computation of scattering observables requires the evaluation of multi-loop integrals and for the computation of observables at the third post-Minkowskian order we analyze the required two-loop integrals. Our discussion uses retarded propagators which impose causal boundary conditions of the observables. Finally we turn to results of the WQFT starting with the gravitational bremsstrahlung of the scattering of two spinning bodies. This waveform is discussed together with its radiative information of linear and angular momentum fluxes. Lastly we present the conservative and radiative impulse and spin kick at third post-Minkowskian order and quadratic order in spins together with the a conservative Hamiltonian at the corresponding perturbative order. The results obey a generalized Bini-Damour radiation-reaction relation and their conservative parts can be parametrized in terms of a single scalar.