Techn. University, Diss., 2001--Dresden.

University, Diss., 2001--Dortmund.

Explaining the baryon asymmetry of the Universe has been a long-standing problem of particle physics, with the consensus being that new physics is required as the Standard Model (SM) cannot resolve this issue. Beyond the Standard Model (BSM) scenarios would need to incorporate new sources of \(CP\) violation and either introduce new departures from thermal equilibrium or modify the existing electroweak phase transition. In this thesis, we explore two approaches to baryogenesis, i.e. the generation of this asymmetry. In the first approach, we study the two-particle irreducible (2PI) formalism as a means to investigate non-equilibrium phenomena. After arriving at the renormalised equations of motions (EOMs) to describe the dynamics of a phase transition, we discuss the techniques required to obtain the various counterterms in an on-shell scheme. To this end, we consider three truncations up to two-loop order of the 2PI effective action: the Hartree approximation, the scalar sunset approximation and the fermionic sunset approximation. We then reconsider the renormalisation procedure in an \(\overline{\text{MS}}\) scheme to evaluate the 2PI effective potential for the aforementioned truncations. In the Hartree and the scalar sunset approximations, we obtain analytic expressions for the various counterterms and subsequently calculate the effective potential by piecing together the finite contributions. For the fermionic sunset approximation, we obtain similar equations for the counterterms in terms of divergent parts of loop integrals. However, these integrals cannot be expressed in an analytic form, making it impossible to evaluate the 2PI effective potential with the fermionic contribution. Our main results are thus related to the renormalisation programme in the 2PI formalism: \( (i) \)the procedure to obtain the renormalised EOMs, now including fermions, which serve as the starting point for the transport equations for electroweak baryogenesis and \( (ii) \) the method to obtain the 2PI effective potential in a transparent manner. In the second approach, we study baryogenesis via leptogenesis. Here, an asymmetry in the lepton sector is generated, which is then converted into the baryon asymmetry via the sphaleron process in the SM. We proceed to consider an extension of the SM along the lines of a scotogenic framework. The newly introduced particles are charged odd under a \(\mathbb{Z}_2\) symmetry, and masses for the SM neutrinos are generated radiatively. The \(\mathbb{Z}_2\) symmetry results in the lightest BSM particle being stable, allowing for a suitable dark matter (DM) candidate. Furthermore, the newly introduced heavy Majorana fermionic singlets provide the necessary sources of \(CP\) violation through their Yukawa interactions and their out-of-equilibrium decays produce a lepton asymmetry. This model is constrained from a wide range of observables, such as consistency with neutrino oscillation data, limits on branching ratios of charged lepton flavour violating decays, electroweak observables and obtaining the observed DM relic density. We study leptogenesis in this model in light of the results of a Markov chain Monte Carlo scan, implemented in consideration of the aforementioned constraints. Successful leptogenesis in this model, to account for the baryon asymmetry, then severely constrains the available parameter space. / Die Erklärung der beobachteten Baryon-Asymmetrie im Universum ist ein seit langem ungelöstes Problem in der Hochenergiephysik. Ein weitgehender Konsens besteht darin, dass dafür "neue Physik" erforderlich ist, da dieses Problem nicht im Rahmen des Standardmodells gelöist werden kann. Dazu gehören CP-verletzende Erweiterungen des Standardmodells ebenso wie neue Aspekte des Nichtgleichgewichts und Modifikationen des elektroschwachen Phasenübergangs. In dieser Dissertation werden zwei Herangehensweisen untersucht, mit denen eine Baryon-Asymmetrie erzeugt werden könnte. Die erste Herangehensweise besteht darin, den 2-Teilchen-irreduziblen (2PI) Formalismus anzuwenden, um auf diese Weise Nichtgleichgewichtsphänomene berücksichtigen zu können. Nach Ableitung der renormierten Bewegungsgleichungen, welche die Dynamik des Phasenübergangs beschreiben, werden Methoden diskutiert, mit denen die sogenannten Counterterme im "On-shell"-Schema berechnet werden können. Um dieses Ziel zu erreichen, betrachten wir drei verschiedene Näherungen der 2PI-Wirkung in zweiter Schleifenordnung, nämlich die Hartree- und die skalare 'sunset' Approximation sowie die fermionische 'sunset'-Approximation. Danach kehren wir zur Renormierungsprozedur in einem \(\overline{\text{MS}}\)-Schema zurück, um das effektive 2PI-Potential für die jeweiligen Abschneideverfahren zu berechnen. In den ersten beiden Fällen gelangen wir zu analytischen Ausdrücken für die verschiedenen Counterterme und berechnen anschließend durch Zusammenfügen aller Beiträge das effektive Potential. Im fermionischen Fall erhalten wir ähnliche Gleichungen für die Counterterme, deren Schleifenintegrale allerdings noch divergente Anteile enthalten. Weil diese Integrale nicht in analytisch geschlossener Form dargestellt werden können, ist es in diesem Fall nicht möglich, das effektive Potential zu berechnen. Die beiden wesentlichen Resultate beziehen sich also auf Renormierungsverfahren im 2PI-Formalismus: \( (i) \) eine Methode, um renormierte Bewegungsgleichungen, jetzt auch mit Fermionen, zu erhalten, die als Ausgangspunkt für Transportgleichungen in der elektroschwachen Baryogenese nutzbringend sein können, und \( (ii) \) eine Methode, um das effektive 2PI-Potential in einer transparenten Weise zu bestimmen. Die zweite Herangehensweise befasst sich mit der Baryogenese durch Leptogenese. In diesem Fall wird zunächst eine Asymmetrie im leptonischen Sektor erzeugt, die dann vermittels eines Sphaleron-Prozesses in eine Baryonasymmetrie konvertiert wird. Wiederum betrachten wir eine Erweiterung des Standardmodells im Sinn eines skotogenen Ansatzes. Die zusätzlich eingeführten Teilchen sind ungerade geladen unter einer \(\mathbb{Z}_2\)-Symmetrie und die Massen für die Neutrinos im Standardmodell werden durch Strahlungskorrekturen erzeugt. Wegen der \(\mathbb Z_2\)-Symmetrie sind die leichtesten Teilchen im erweiterten Standardmodell stabil und kommen damit als geeignete Kandidaten für dunkle Materie infrage. Darüber hinaus verursachen die zusätzlich eingeführten schweren Majorana-Singlet-Fermionen durch ihre Yukawa-Wechselwirkung die benötigte CP-Verletzung, wobei Zerfälle im Nichtgleichgewicht zu einer Leptonen-Asymmetrie führen. Dieses Model wird durch eine Vielzahl von Observablen eingeschränkt, wie z.B. Konsistenz mit den Daten zu Neutrino-Oszillationen, Schranken der Verzweigungsverhältnisse für leptonische Flavor-verletzende Zerfälle, elektroschwache Präzisionsobservablen sowie die im Universum beobachtete Dichte dunkler Materie. Wir untersuchen die Leptogenese im Rahmen dieses Modells in einem Parameterraumbereich, der mithilfe einer Makovketten-Monte-Carlo-Simulation die unter Berücksichtigung der genannten Einschränkungen bestimmt wurde. Eine erfolgreiche Leptogenese in diesem Modell, welche auf die gewünschte Baryon-Asymmetrie führt, schränkt dann den Parameterraum erheblich weiter ein.

This thesis is devoted to the investigation of the phenomenon of quantum radiation -- i.e. the conversion of the (virtual) quantum fluctuations of a quantised field into (real) particles owing to the influence of external conditions. For that purpose a canonical particle (and thereby vacuum) definition is presented for a quantum field in the presence of specific external conditions. Utilising this set-up the number of Rindler particles in the Minkowski vacuum is calculated explicitly where the Unruh effect is recovered. Focusing on the gravitational collapse of an object the number of created particles accounting for the Hawking effect is derived and the dependence of the results on the dynamics of the collapse is discussed. Furthermore the influence of finite initial temperatures is investigated for a weakly time-dependent perfectly conducting cavity (dynamical Casimir effect), a dynamical dielectric medium, and the Friedmann-Robertson-Walker metric. Finally the problems arising from the consideration of interacting fields are outlined by means of a simple example.

Konstanz, Univ., Diplomarb., 2002.

The goal of this Thesis is to give a presentation of some key issues regarding the non-perturbative renormalization of the periodic scalar field theories. As an example of the non-perturbative methods, we use the differential renormalization group approach, particularly the Wegner-Houghton and the Polchinski renormalization group equations, in order to investigate the renormalization of a one-component periodic scalar field theory. The Wegner-Houghton equation provides a resummation of the loop-expansion, and the Polchinski equation is based on the resummation of the perturbation series. Therefore, these equations are exact in the sense that they contain all quantum corrections. In the framework of these renormalization group equations, field theories with periodic self interaction can be considered without violating the essential symmetry of the model: the periodicity. Both methods - the Wegner-Houghton and the Polchinski approaches - are inspired by Wilson's blocking construction in momentum space: the Wegner-Houghton method uses a sharp momentum cut-off and thus cannot be applied directly to non-constant fields (contradicts with the "derivative expansion"); the Polchinski method is based on a smooth cut-off and thus gives rise naturally to a "derivative expansion" for varying fields. However, the shape of the cut-off function (the "scheme") is not fixed a priori within Polchinski's ansatz. In this thesis, we compare the Wegner--Houghton and the Polchinski equation; we demonstrate the consistency of both methods for near-constant fields in the linearized level and obtain constraints on the regulator function that enters into Polchinski's equation. Analytic and numerical results are presented which illustrate the renormalization group flow for both methods. We also briefly discuss the relation of the momentum-space methods to real-space renormalization group approaches. For the two-dimensional Coulomb gas (which is investigated by a real-space renormalization group method using the dilute-gas approximation), we provide a systematic method for obtaining higher-order corrections to the dilute gas result.

The accurate calculation of atomic spectra, including radiative corrections, is one of the rather challenging tasks in theoretical physics. The entire formalism of quantum (gauge) field theory, augmented by the difficulties of the bound-state formalism, is needed for an accurate understanding of the relevant physics at the level of current high-precision spectroscopy. In this thesis, several calculations in this area are described in detail. Investigations on large-order perturbation-theory effects (and predictive limits of perturbation theory) supplement these investigations. In the context of applications, numerical algorithms for the acceleration of the convergence of series are discussed.

No description available.

The goal of this Thesis is to give a presentation of some key issues regarding the non-perturbative renormalization of the periodic scalar field theories. As an example of the non-perturbative methods, we use the differential renormalization group approach, particularly the Wegner-Houghton and the Polchinski renormalization group equations, in order to investigate the renormalization of a one-component periodic scalar field theory. The Wegner-Houghton equation provides a resummation of the loop-expansion, and the Polchinski equation is based on the resummation of the perturbation series. Therefore, these equations are exact in the sense that they contain all quantum corrections. In the framework of these renormalization group equations, field theories with periodic self interaction can be considered without violating the essential symmetry of the model: the periodicity. Both methods - the Wegner-Houghton and the Polchinski approaches - are inspired by Wilson's blocking construction in momentum space: the Wegner-Houghton method uses a sharp momentum cut-off and thus cannot be applied directly to non-constant fields (contradicts with the "derivative expansion"); the Polchinski method is based on a smooth cut-off and thus gives rise naturally to a "derivative expansion" for varying fields. However, the shape of the cut-off function (the "scheme") is not fixed a priori within Polchinski's ansatz. In this thesis, we compare the Wegner--Houghton and the Polchinski equation; we demonstrate the consistency of both methods for near-constant fields in the linearized level and obtain constraints on the regulator function that enters into Polchinski's equation. Analytic and numerical results are presented which illustrate the renormalization group flow for both methods. We also briefly discuss the relation of the momentum-space methods to real-space renormalization group approaches. For the two-dimensional Coulomb gas (which is investigated by a real-space renormalization group method using the dilute-gas approximation), we provide a systematic method for obtaining higher-order corrections to the dilute gas result.

The accurate calculation of atomic spectra, including radiative corrections, is one of the rather challenging tasks in theoretical physics. The entire formalism of quantum (gauge) field theory, augmented by the difficulties of the bound-state formalism, is needed for an accurate understanding of the relevant physics at the level of current high-precision spectroscopy. In this thesis, several calculations in this area are described in detail. Investigations on large-order perturbation-theory effects (and predictive limits of perturbation theory) supplement these investigations. In the context of applications, numerical algorithms for the acceleration of the convergence of series are discussed.