A non-commutative QFT at the self-dual point

In dieser Diplomarbeit wird das Grosse-Wulkenhaar-Modell am selbstdualen Punkt Omega = 1 behandelt. Die relevanten 2- und 4-Punkt-Feynmangraphen werden bis zur zweiten Loop-Ordnung renormalisiert um die Beschränktheit der Betafunktion zu zeigen. Dies wird erreicht in dem man zeigt, dass die Differenz zwischen nackter und renormalisierter Kopplungskonstante endlich ist. Dieses Resultat wird danach bis zu allen Loop-Ordnungen verallgemeinert durch Verwendung von Ward-Identitäten und der Dyson-Schwinger-Gleichung. Zusätzlich werden die erhaltenen Relationen zwischen 2- und 4-Punkt-Funktionen explizit berechnet. Im letzten Teil werden die Techniken des allgemeinen Beweises benutzt um die Beschränktheit der Beta-Funktion für das Langmann-Szabo-Zarembo Modell zu zeigen.In this tesis the Grosse-Wulkenhaar-model at the self-dual point = 1 is examined. The relevant 2-point and 4-point Feynman graphs are renormalized up to two loop order to proof the boundedness of the Beta-function by showing that the difference between bare and renormalized coupling constant is finite. This result is then generalized up to all orders by using Ward-Identites and the Dyson-Schwinger-Equation. Additionally the relations between (2n-2)- and 2n-point functions, obtained through the Ward-Identities, are calculated explicitly between 2 and 4-point functions. The last section uses the techniques of the general proof to show the boundedness of the Beta-function of the Grosse- Wulkenhaar-model in a magnetic field, namely the Langmann-Szabo-Zarembo model with oscillator term, which is an interesting toy model of the Quantum Hall Effect

Nucleon distribution amplitudes from lattice QCD

We calculate low moments of the leading-twist and next-to-leading twist nucleon distribution amplitudes on the lattice using two flavors of clover fermions. The results are presented in the MSbar scheme at a scale of 2 GeV and can be immediately applied in phenomenological studies. We find that the deviation of the leading-twist nucleon distribution amplitude from its asymptotic form is less pronounced than sometimes claimed in the literature.Comment: 5 pages, 3 figures, 2 tables. RevTeX style. Normalization for \lambda_i corrected. Discussion of the results extended. To be published in PR

Non-perturbative renormalization of three-quark operators

High luminosity accelerators have greatly increased the interest in semi-exclusive and exclusive reactions involving nucleons. The relevant theoretical information is contained in the nucleon wavefunction and can be parametrized by moments of the nucleon distribution amplitudes, which in turn are linked to matrix elements of local three-quark operators. These can be calculated from first principles in lattice QCD. Defining an RI-MOM renormalization scheme, we renormalize three-quark operators corresponding to low moments non-perturbatively and take special care of the operator mixing. After performing a scheme matching and a conversion of the renormalization scale we quote our final results in the MSbar scheme at mu=2 GeV.Comment: 49 pages, 3 figure

Flexible high efficiency perovskite solar cells

Flexible perovskite based solar cells with power conversion efficiencies of 7% have been prepared on PET based conductive substrates. Extended bending of the devices does not deteriorate their performance demonstrating their suitability for roll to roll processing

Hadron structure from lattice quantum chromodynamics

This is a review of hadron structure physics from lattice QCD. Throughout this report, we place emphasis on the contribution of lattice results to our understanding of a number of fundamental physics questions related to, e.g., the origin and distribution of the charge, magnetization, momentum and spin of hadrons. Following an introduction to some of the most important hadron structure observables, we summarize the methods and techniques employed for their calculation in lattice QCD. We briefly discuss the status of relevant chiral perturbation theory calculations needed for controlled extrapolations of the lattice results to the physical point. In the main part of this report, we give an overview of lattice calculations on hadron form factors, moments of (generalized) parton distributions, moments of hadron distribution amplitudes, and other important hadron structure observables. Whenever applicable, we compare with results from experiment and phenomenology, taking into account systematic uncertainties in the lattice computations. Finally, we discuss promising results based on new approaches, ideas and techniques, and close with remarks on future perspectives of the field.Comment: 189 pages, to be published in Physics Report

Renormalization of three-quark operators for the nucleon distribution amplitude

High luminosity accelerators have greatly increased the interest in semi-exclusive and exclusive reactions involving nucleons. The relevant theoretical information is contained in the nucleon wavefunction and can be parametrized by moments of the nucleon distribution amplitudes, which in turn are linked to matrix elements of local three-quark operators. These can be calculated from first principles in lattice QCD. Defining an RI-MOM renormalization scheme, we renormalize three-quark operators corresponding to low moments non-perturbatively and take special care of the operator mixing. After performing a scheme matching and a conversion of the renormalization scale we quote our final results for the low moments of the nucleon distribution amplitude in the MS scheme at mu = 2GeV

Emergent Phenomena in Matrix Models

In this work we perform a careful study of different matrix models and particularly the property of emergent phenomena in them. We start discussing a 2-matrix model of Yang-Mills type that exhibits an emergent topology in the strong coupling limit. We use Monte-Carlo simulations to obtain various observables that allow us to get more insight in the transition from the non-commutative regime towards the commutative, strong coupling, limit. We will continue to discuss higher dimensional Yang-Mills matrix models, focusing on the lowest dimensional case that is well defned, D = 3, and on the large-D limit. While we discuss the possibility of an emergent topology in 3 dimensions, we find that the behaviour of this type of models changes towards random matrices for large D. In the second part of the thesis we will add a Myers term to the Yang-Mills type models which extends the possible solutions to the model by fuzzy spaces. We carry out a 1-loop calculation for a general SU(d) symmetric solution to this class of models. We will then turn to a numerical study of a model that incorporates the simplest case of a fuzzy manifold, the fuzzy sphere. We will further study fuzzy CP2 which appears as a solution to the 8-dimensional Yang-Mills-Myers model. Numerical results from a Monte-Carlo simulation will be used to compare with the analytical results obtained earlier. We will further construct a slightly modified 8-dimensional model that has a fuzzy complex projective plane as the ground state in phase space. In total, we find four different phases in this model, which we will describe in detail after numerically mapping the phase diagram