Investigations on asymptotic safety of metric, tetrad and Einstein-Cartan gravity

Among the different approaches for a construction of a fundamental quantum theory of gravity the Asymptotic Safety scenario conjectures that quantum gravity can be defined within the framework of conventional quantum field theory, but only non-perturbatively. In this case its high energy behavior is controlled by a non-Gaussian fixed point of the renormalization group flow, such that its infinite cutoff limit can be taken in a well defined way. A theory of this kind is referred to as non-perturbatively renormalizable. In the last decade a considerable amount of evidence has been collected that in four dimensional metric gravity such a fixed point, suitable for the Asymptotic Safety construction, indeed exists. This thesis extends the Asymptotic Safety program of quantum gravity by three independent studies that differ in the fundamental field variables the investigated quantum theory is based on, but all exhibit a gauge group of equivalent semi-direct product structure. It allows for the first time for a direct comparison of three asymptotically safe theories of gravity constructed from different field variables. The first study investigates metric gravity coupled to SU(N) Yang-Mills theory. In particular the gravitational effects to the running of the gauge coupling are analyzed and its implications for QED and the Standard Model are discussed. The second analysis amounts to the first investigation on an asymptotically safe theory of gravity in a pure tetrad formulation. Its renormalization group flow is compared to the corresponding approximation of the metric theory and the influence of its enlarged gauge group on the UV behavior of the theory is analyzed. The third study explores Asymptotic Safety of gravity in the Einstein-Cartan setting. Here, besides the tetrad, the spin connection is considered a second fundamental field. The larger number of independent field components and the enlarged gauge group render any RG analysis of this system much more difficult than the analog metric analysis. In order to reduce the complexity of this task a novel functional renormalization group equation is proposed, that allows for an evaluation of the flow in a purely algebraic manner. As a first example of its suitability it is applied to a three dimensional truncation of the form of the Holst action, with the Newton constant, the cosmological constant and the Immirzi parameter as its running couplings. A detailed comparison of the resulting renormalization group flow to a previous study of the same system demonstrates the reliability of the new equation and suggests its use for future studies of extended truncations in this framework.

Structural and strain analysis in the Late Paleozoic coastal accretionary wedge of central Chile

Abstract In this study structural and finite strain data are used to explore the tectonic evolution and the exhumation history of the Chilean accretionary wedge. The Chilean accretionary wedge is part of a Late Paleozoic subduction complex that developed during subduction of the Pacific plate underneath South America. The wedge is commonly subdivided into a structurally lower Western Series and an upper Eastern Series. This study shows the progressive development of structures and finite strain from the least deformed rocks in the eastern part of the Eastern Series of the accretionary wedge to higher grade schist of the Western Series at the Pacific coast. Furthermore, this study reports finite-strain data to quantify the contribution of vertical ductile shortening to exhumation. Vertical ductile shortening is, together with erosion and normal faulting, a process that can aid the exhumation of high-pressure rocks. In the east, structures are characterized by upright chevron folds of sedimentary layering which are associated with a penetrative axial-plane foliation, S1. As the F1 folds became slightly overturned to the west, S1 was folded about recumbent open F2 folds and an S2 axial-plane foliation developed. Near the contact between the Western and Eastern Series S2 represents a prominent subhorizontal transposition foliation. Towards the structural deepest units in the west the transposition foliation became progressively flat lying. Finite-strain data as obtained by Rf/Phi and PDS analysis in metagreywacke and X-ray texture goniometry in phyllosilicate-rich rocks show a smooth and gradual increase in strain magnitude from east to west. There are no evidences for normal faulting or significant structural breaks across the contact of Eastern and Western Series. The progressive structural and strain evolution between both series can be interpreted to reflect a continuous change in the mode of accretion in the subduction wedge. Before ~320-290 Ma the rocks of the Eastern Series were frontally accreted to the Andean margin. Frontal accretion caused horizontal shortening and upright folds and axial-plane foliations developed. At ~320-290 Ma the mode of accretion changed and the rocks of the Western Series were underplated below the Andean margin. This basal accretion caused a major change in the flow field within the wedge and gave rise to vertical shortening and the development of the penetrative subhorizontal transposition foliation. To estimate the amount that vertical ductile shortening contributed to the exhumation of both units finite strain is measured. The tensor average of absolute finite strain yield Sx=1.24, Sy=0.82 and Sz=0.57 implying an average vertical shortening of ca. 43%, which was compensated by volume loss. The finite strain data of the PDS measurements allow to calculate an average volume loss of 41%. A mass balance approximates that most of the solved material stays in the wedge and is precipitated in quartz veins. The average of relative finite strain is Sx=1.65, Sy=0.89 and Sz=0.59 indicating greater vertical shortening in the structurally deeper units. A simple model which integrates velocity gradients along a vertical flow path with a steady-state wedge is used to estimate the contribution of deformation to ductile thinning of the overburden during exhumation. The results show that vertical ductile shortening contributed 15-20% to exhumation. As no large-scale normal faults have been mapped the remaining 80-85% of exhumation must be due to erosion.

Structure formation of amphiphilic molecules at the air,water interface and after film transfer

One of the basic concepts of molecular self-assembly is that the morphology of the aggregate is directly related to the structure and interaction of the aggregating molecules. This is not only true for the aggregation in bulk solution, but also for the formation of Langmuir films at the air/water interface. Thus, molecules at the interface do not necessarily form flat monomolecular films but can also aggregate into multilayers or surface micelles. In this context, various novel synthetic molecules were investigated in terms of their morphology at the air/water interface and in transferred films. rnFirst, the self-assembly of semifluorinated alkanes and their molecular orientation at the air/water interface and in transferred films was studied employing scanning force microscopy (SFM) and Kelvin potential force microscopy. Here it was found, that the investigated semifluorinated alkanes aggregate to form circular surface micelles with a diameter of 30 nm, which are constituted of smaller muffin-shaped subunits with a diameter of 10 nm. A further result is that the introduction of an aromatic core into the molecular structure leads to the formation of elongated surface micelles and thus implements a directionality to the self-assembly. rnSecond, the self-assembly of two different amphiphilic hybrid materials containing a short single stranded desoxyribonucleic acid (DNA) sequence was investigated at the air/water interface. The first molecule was a single stranded DNA (11mer) molecule with two hydrophobically modified 5-(dodec-1-ynyl)uracil nucleobases at the terminal 5'-end of the oligonucleotide sequence. Isotherm measurements revealed the formation of semi-stable films at the air/water interface. SFM imaging of films transferred via Langmuir-Blodgett technique supported this finding and indicated mono-, bi- and multilayer formation, according to the surface pressure applied upon transfer. Within these films, the hydrophilic DNA sequence was oriented towards air covering 95% of the substrate.rnSimilar results were obtained with a second type of amphiphile, a DNA block copolymer. Furthermore, the potential to perform molecular recognition experiments at the air/water interface with these DNA hybrid materials was evaluated.rnThird, polyglycerol ester molecules (PGE), which are known to form very stable foams, were studies. Aim was to elucidate the molecular structure of PGE molecules at the air/water interface in order to comprehend the foam stabilization mechanism. Several model systems mimicking the air/water interface of a PGE foam and methods for a noninvasive transfer were tested and characterized by SFM. It could be shown, that PGE stabilizes the air/water interface of a foam bubble by formation of multiple surfactant layers. Additionally, a new transfer technique, the bubble film transfer was established and characterized by high speed camera imaging.The results demonstrate the diversity of structures, which can be formed by amphiphilic molecules at the air/water interface and after film transfer, as well as the impact of the chemical structure on the aggregate morphology.