A novel functional renormalization group framework for gauge theories and gravity

In this thesis we develop further the functional renormalization group (RG) approach to quantum field theory (QFT) based on the effective average action (EAA) and on the exact flow equation that it satisfies. The EAA is a generalization of the standard effective action that interpolates smoothly between the bare action for krightarrowinfty and the standard effective action rnfor krightarrow0. In this way, the problem of performing the functional integral is converted into the problem of integrating the exact flow of the EAA from the UV to the IR. The EAA formalism deals naturally with several different aspects of a QFT. One aspect is related to the discovery of non-Gaussian fixed points of the RG flow that can be used to construct continuum limits. In particular, the EAA framework is a useful setting to search for Asymptotically Safe theories, i.e. theories valid up to arbitrarily high energies. A second aspect in which the EAA reveals its usefulness are non-perturbative calculations. In fact, the exact flow that it satisfies is a valuable starting point for devising new approximation schemes. In the first part of this thesis we review and extend the formalism, in particular we derive the exact RG flow equation for the EAA and the related hierarchy of coupled flow equations for the proper-vertices. We show how standard perturbation theory emerges as a particular way to iteratively solve the flow equation, if the starting point is the bare action. Next, we explore both technical and conceptual issues by means of three different applications of the formalism, to QED, to general non-linear sigma models (NLsigmaM) and to matter fields on curved spacetimes. In the main part of this thesis we construct the EAA for non-abelian gauge theories and for quantum Einstein gravity (QEG), using the background field method to implement the coarse-graining procedure in a gauge invariant way. We propose a new truncation scheme where the EAA is expanded in powers of the curvature or field strength. Crucial to the practical use of this expansion is the development of new techniques to manage functional traces such as the algorithm proposed in this thesis. This allows to project the flow of all terms in the EAA which are analytic in the fields. As an application we show how the low energy effective action for quantum gravity emerges as the result of integrating the RG flow. In any treatment of theories with local symmetries that introduces a reference scale, the question of preserving gauge invariance along the flow emerges as predominant. In the EAA framework this problem is dealt with the use of the background field formalism. This comes at the cost of enlarging the theory space where the EAA lives to the space of functionals of both fluctuation and background fields. In this thesis, we study how the identities dictated by the symmetries are modified by the introduction of the cutoff and we study so called bimetric truncations of the EAA that contain both fluctuation and background couplings. In particular, we confirm the existence of a non-Gaussian fixed point for QEG, that is at the heart of the Asymptotic Safety scenario in quantum gravity; in the enlarged bimetric theory space where the running of the cosmological constant and of Newton's constant is influenced by fluctuation couplings.

Influence of spatial constraints in non-crystalline regions on the polymer dynamics in semi-crystalline polyethylene: a solid state NMR study

A broad variety of solid state NMR techniques were used to investigate the chain dynamics in several polyethylene (PE) samples, including ultrahigh molecular weight PEs (UHMW-PEs) and low molecular weight PEs (LMW-PEs). Via changing the processing history, i.e. melt/solution crystallization and drawing processes, these samples gain different morphologies, leading to different molecular dynamics. Due to the long chain nature, the molecular dynamics of polyethylene can be distinguished in local fluctuation and long range motion. With the help of NMR these different kinds of molecular dynamics can be monitored separately. In this work the local chain dynamics in non-crystalline regions of polyethylene samples was investigated via measuring 1H-13C heteronuclear dipolar coupling and 13C chemical shift anisotropy (CSA). By analyzing the motionally averaged 1H-13C heteronuclear dipolar coupling and 13C CSA, the information about the local anisotropy and geometry of motion was obtained. Taking advantage of the big difference of the 13C T1 relaxation time in crystalline and non-crystalline regions of PEs, the 1D 13C MAS exchange experiment was used to investigate the cooperative chain motion between these regions. The different chain organizations in non-crystalline regions were used to explain the relationship between the local fluctuation and the long range motion of the samples. In a simple manner the cooperative chain motion between crystalline and non-crystalline regions of PE results in the experimentally observed diffusive behavior of PE chain. The morphological influences on the diffusion motion have been discussed. The morphological factors include lamellar thickness, chain organization in non-crystalline regions and chain entanglements. Thermodynamics of the diffusion motion in melt and solution crystallized UHMW-PEs is discussed, revealing entropy-controlled features of the chain diffusion in PE. This thermodynamic consideration explains the counterintuitive relationship between the local fluctuation and the long range motion of the samples. Using the chain diffusion coefficient, the rates of jump motion in crystals of the melt crystallized PE have been calculated. A concept of "effective" jump motion has been proposed to explain the difference between the values derived from the chain diffusion coefficients and those in literatures. The observations of this thesis give a clear demonstration of the strong relationship between the sample morphology and chain dynamics. The sample morphologies governed by the processing history lead to different spatial constraints for the molecular chains, leading to different features of the local and long range chain dynamics. The knowledge of the morphological influence on the microscopic chain motion has many implications in our understanding of the alpha-relaxation process in PE and the related phenomena such as crystal thickening, drawability of PE, the easy creep of PE fiber, etc.

Geochemistry, petrogenesis and tectonic setting of ophiolites and mafic-ultramafic complexes in the Northeastern Aegean Region

In this study two ophiolites and a mafic-ultramafic complexes of the northeastern Aegean Sea, Greece, have been investigated to re-evaluate their petrogenetic evolution and tectonic setting. These complexes are: the mafic-ultramafic complex of Lesvos Island and the ophiolites of Samothraki Island and the Evros area. In order to examine these complexes in detail whole-rock major- and trace-elements as well as Sr and Nd isotopes, and minerals were analysed and U-Pb SHRIMP ages on zircons were determined. The mafic-ultramafic complex of Lesvos Island consists of mantle peridotite thrusted over a tectonic mélange containing metasediments, metabasalts and a few metagabbros. This succession had previously been interpreted as an ophiolite of Late Jurassic age. The new field and geochemical data allow a reinterpretation of this complex as representing an incipient continental rift setting that led to the subsequent formation of the Meliata-Maliac-Vardar branches of Neotethys in Upper Permian times (253 ± 6 Ma) and the term “Lesvos ophiolite” should be abandoned. With proceeding subduction and closure of the Maliac Ocean in Late Jurassic times (155 Ma) the Lesvos mafic-ultramafic complex was obducted. Zircon ages of 777, 539 and 338 Ma from a gabbro strongly suggest inheritance from the intruded basement and correspond to ages of distinct terranes recently recognized in the Hellenides (e.g. Florina terrane). Geochemical similar complexes which contain rift associations with Permo-Triassic ages can be found elsewhere in Greece and Turkey, namely the Teke Dere Thrust Sheet below the Lycian Nappes (SW Turkey), the Pindos subophiolitic mélange (W Greece), the Volcanosedimentary Complex on Central Evia Island (Greece) and the Karakaya Complex (NW Turkey). This infers that the rift-related rocks from Lesvos belong to an important Permo-Triassic rifting episode in the eastern Mediterranean. The ‘in-situ’ ophiolite of Samothraki Island comprises gabbros, sparse dykes and basalt flows as well as pillows cut by late dolerite dykes and had conventionally been interpreted as having formed in an ensialic back-arc basin. The results of this study revealed that none of the basalts and dolerites resemble mid-ocean ridge or back-arc basin basalts thus suggesting that the Samothraki ophiolite cannot represent mature back-arc basin crust. The age of the complex is regarded to be 160 ± 5 Ma (i.e. Oxfordian; early Upper Jurassic), which precludes any correlation with the Lesvos mafic-ultramafic complex further south (253 ± 6 Ma; Upper Permian). Restoration of the block configuration in NE Greece, before extensional collapse of the Hellenic hinterland and exhumation of the Rhodope Metamorphic Core Complex (mid-Eocene to mid-Miocene), results in a continuous ophiolite belt from Guevgueli in the NW to Samothraki in the SE, thus assigning the latter to the Innermost Hellenic Ophiolite Belt. In view of the data of this study, the Samothraki ophiolite represents a rift propagation of the Sithonia ophiolite spreading ridge into the Chortiatis calc-alkaline arc. The ophiolite of the Evros area consists of a plutonic sequence comprising cumulate and non-cumulate gabbros with plagiogranite veins, and an extrusive sequence of basalt dykes, massive and pillow lavas as well as pyroclastic rocks. Furthermore, in the Rhodope Massif tectonic lenses of harzburgites and dunites can be found. All rocks are spatially separated. The analytical results of this study revealed an intra-oceanic island arc setting for the Evros ophiolitic rocks. During late Middle Jurassic times (169 ± 2 Ma) an intra-oceanic arc has developed above a northwards directed intra-oceanic subduction zone of the Vardar Ocean in front of the Rhodope Massif. The boninitic, island arc tholeiitic and calc-alkaline rocks reflect the evolution of the Evros island arc. The obduction of the ophiolitic rocks onto the Rhodope basement margin took place during closure of the Vardar ocean basins. The harzburgites and dunites of the Rhodope Massif are strongly depleted and resemble harzburgites from recent oceanic island arcs. After melt extraction they underwent enrichment processes by percolating melts and fluids from the subducted slab. The relationship of the peridotites and the Evros ophiolite is still ambiguous, but the stratigraphic positions of the peridotites and the ophiolitic rocks indicate separated origin. The harzburgites and dunites most probably represent remnants of the mantle wedge of the island arc of the Rhodope terrane formed above subducted slab of the Nestos Ocean in late Middle Jurassic times. During collision of the Thracia terrane with the Rhodope terrane thrusting of the Rhodope terrane onto the Thracia terrane took place, whereas the harzburgites and dunites were pushed between the two terranes now cropping out on top of the Thracia terrane of the Rhodope Massif.

Optical resonances of sphere-on-plane geometries

The optical resonances of metallic nanoparticles placed at nanometer distances from a metal plane were investigated. At certain wavelengths, these “sphere-on-plane” systems become resonant with the incident electromagnetic field and huge enhancements of the field are predicted localized in the small gaps created between the nanoparticle and the plane. An experimental architecture to fabricate sphere-on-plane systems was successfully achieved in which in addition to the commonly used alkanethiols, polyphenylene dendrimers were used as molecular spacers to separate the metallic nanoparticles from the metal planes. They allow for a defined nanoparticle-plane separation and some often are functionalized with a chromophore core which is therefore positioned exactly in the gap. The metal planes used in the system architecture consisted of evaporated thin films of gold or silver. Evaporated gold or silver films have a smooth interface with their substrate and a rougher top surface. To investigate the influence of surface roughness on the optical response of such a film, two gold films were prepared with a smooth and a rough side which were as similar as possible. Surface plasmons were excited in Kretschmann configuration both on the rough and on the smooth side. Their reflectivity could be well modeled by a single gold film for each individual measurement. The film has to be modeled as two layers with significantly different optical constants. The smooth side, although polycrystalline, had an optical response that was very similar to a monocrystalline surface while for the rough side the standard response of evaporated gold is retrieved. For investigations on thin non-absorbing dielectric films though, this heterogeneity introduces only a negligible error. To determine the resonant wavelength of the sphere-on-plane systems a strategy was developed which is based on multi-wavelength surface plasmon spectroscopy experiments in Kretschmann-configuration. The resonant behavior of the system lead to characteristic changes in the surface plasmon dispersion. A quantitative analysis was performed by calculating the polarisability per unit area /A treating the sphere-on-plane systems as an effective layer. This approach completely avoids the ambiguity in the determination of thickness and optical response of thin films in surface plasmon spectroscopy. Equal area densities of polarisable units yielded identical response irrespective of the thickness of the layer they are distributed in. The parameter range where the evaluation of surface plasmon data in terms of /A is applicable was determined for a typical experimental situation. It was shown that this analysis yields reasonable quantitative agreement with a simple theoretical model of the sphere-on-plane resonators and reproduces the results from standard extinction experiments having a higher information content and significantly increased signal-to-noise ratio. With the objective to acquire a better quantitative understanding of the dependence of the resonance wavelength on the geometry of the sphere-on-plane systems, different systems were fabricated in which the gold nanoparticle size, type of spacer and ambient medium were varied and the resonance wavelength of the system was determined. The gold nanoparticle radius was varied in the range from 10 nm to 80 nm. It could be shown that the polyphenylene dendrimers can be used as molecular spacers to fabricate systems which support gap resonances. The resonance wavelength of the systems could be tuned in the optical region between 550 nm and 800 nm. Based on a simple analytical model, a quantitative analysis was developed to relate the systems’ geometry with the resonant wavelength and surprisingly good agreement of this simple model with the experiment without any adjustable parameters was found. The key feature ascribed to sphere-on-plane systems is a very large electromagnetic field localized in volumes in the nanometer range. Experiments towards a quantitative understanding of the field enhancements taking place in the gap of the sphere-on-plane systems were done by monitoring the increase in fluorescence of a metal-supported monolayer of a dye-loaded dendrimer upon decoration of the surface with nanoparticles. The metal used (gold and silver), the colloid mean size and the surface roughness were varied. Large silver crystallites on evaporated silver surfaces lead to the most pronounced fluorescence enhancements in the order of 104. They constitute a very promising sample architecture for the study of field enhancements.

Chemical composition measurements of cloud condensation nuclei and ice nuclei by aerosol mass spectrometry

In this study the Aerodyne Aerosol Mass Spectrometer (AMS) was used during three laboratory measurement campaigns, FROST1, FROST2 and ACI-03. The FROST campaigns took place at the Leipzig Aerosol Cloud Interaction Simulator (LACIS) at the IfT in Leipzig and the ACI-03 campaign was conducted at the AIDA facility at the Karlsruhe Institute of Technology (KIT). In all three campaigns, the effect of coatings on mineral dust ice nuclei (IN) was investigated. During the FROST campaigns, Arizona Test Dust (ATD) particles of 200, 300 and 400 nm diameter were coated with thin coatings (< 7 nm) of sulphuric acid. At these very thin coatings, the AMS was operated close to its detection limits. Up to now it was not possible to accurately determine AMS detection limits during regular measurements. Therefore, the mathematical tools to analyse the detection limits of the AMS have been improved in this work. It is now possible to calculate detection limits of the AMS under operating conditions, without losing precious time by sampling through a particle filter. The instrument was characterised in more detail to enable correct quantification of the sulphate loadings on the ATD particle surfaces. Correction factors for the instrument inlet transmission, the collection efficiency, and the relative ionisation efficiency have been determined. With these corrections it was possible to quantify the sulphate mass per particle on the ATD after the condensation of sulphuric acid on its surface. The AMS results have been combined with the ice nucleus counter results. This revealed that the IN-efficiency of ATD is reduced when it is coated with sulphuric acid. The reason for this reduction is a chemical reaction of sulphuric acid with the particle's surface. These reactions are increasingly taking place when the aerosol is humidified or heated after the coating with sulphuric acid. A detailed analysis of the solubility and the evaporation temperature of the surface reaction products revealed that most likely aluminium sulphate is produced in these reactions.

Das aktuelle Debattenbuch im politischen Feld : eine Analyse anhand von Fallbeispielen /// Arbeitsblätter für die Sachbuchforschung ; 19

Diese Forschungsarbeit zeigt erstmalig anhand von drei Fallbeispielen [„Lob der Disziplin. Eine Streitschrift“ von Bernhard Bueb, „Das Methusalem-Komplott“ von Frank Schirrmacher und „Deutschland schafft sich ab“ von Thilo Sarrazin] und aufbauend auf Bourdieus Theorie des politischen Feldes welche Wirkung s. g. Debattenbücher auf das gesellschaftliche Diskursfeld, die Politik und die Wissenschaft haben können. Die Arbeit gliedert sich in drei Teile. In einem ersten Schritt werden Unterschiede und Gemeinsamkeiten der Autoren und Werke herausgearbeitet. Es wird gezeigt welche Inszenierungsstrategien vorliegen und wie diese den Autor auf das Kräftemessen im politischen Feld vorbereiten. Im Anschluss wird im zweiten Schritt geklärt, wie sich der Autor im politischen Feld positioniert und welchen Einfluss er auf das bestehende Kräfteverhältnis politischer Akteure ausübt. Im letzten Schritt wird diesem Einfluss abstrahierend auf das gesellschaftliche Wirkungspotenzial von Debattenbüchern geschlossen. Unter Zuhilfenahme von Zeitungsartikeln, die bis zu 6 Monaten nach Erscheinungstermin des jeweiligen Titels, in Der Spiegel, Die Zeit und der Frankfurter Allgemeine Sonntagszeitung veröffentlicht wurden, wurde klar, dass Debattenbücher dann erfolgreich sind, wenn sie eine Meinung, die konträr zum gesellschaftlichen Konsens steht, provokativ und emotional aufbereiten und der Autor bereit ist, als Meinungsträger seine Thesen in der öffentlichen Debatte zu vertreten. So gestaltet regt das Debattenbuch – auch wenn es langfristig keinen Effekt auf das zentrale gesellschaftliche Diskursfeld hat - zur „Selbstfindung durch Emotionen“ an. Auf vermeintliche Sachlichkeit anspielend wirkt es, weil es den Lesern gesellschaftliche Konfliktherde auf emotionalem Wege bewusst werden lässt und so Impulse zur Veränderung setzt.

Hexenfieber im Erzgebirge - Die Annaberger Krankheit 1712 - 1720

Die Arbeit untersucht das seuchenartige Auftreten von Besessenheitsfällen in Annaberg (Erzgebirge) in den Jahren 1713-1720, die Auslöser der letzten Hexenprozesse in Kursachsen waren. Zeitgenössische Beobachter stritten intensiv, ob diese sogenannte „Annaberger Krankheit“ durch Zauberei verursacht oder eine psychosomatisch bedingte Massenerkrankung war. In Abkehr von dem Vorurteil, alle Betroffenen einer solchen Massenhysterie litten an derselben Erkrankung, werden diverse Krankengeschichten rekonstruiert. Indem sich dabei Elemente von Rollenspielen (Kinderhexen, Hysterie) und Betrug (Almosenerschleichung, Denunziationen, politisch motivierte Inszenierungen) finden, zeigt sich die wundersame „Krankheit“ als nicht pathologischer sondern sozialer Vorgang. rnAm dessen Beginn stand die Geburt der Interpretation, es gäbe eine außergewöhnliche Krankheit in der Stadt, wozu akzidentielle Ereignisse mehr beitrugen als auffällige Krankheitsfälle. Gerüchtbildung und politische Instrumentalisierung bildeten den Rahmen für den Einstieg von Nachahmern, die das fiktive Krankheitsbild in die Realität eines demonstrativen Schauspiel umsetzten. Dieser Mechanismus eines selbsterfüllenden Menetekels wird vor dem Hintergrund seiner kulturellen, sozialen, ökonomischen und historischen Bedingungen detailliert rekonstruiert.