Introduction to the functional RG and applications to gauge theories

These lectures contain an introduction to modern renormalization group (RG) methods as well as functional RG approaches to gauge theories. In the first lecture, the functional renormalization group is introduced with a focus on the flow equation for the effective average action. The second lecture is devoted to a discussion of flow equations and symmetries in general, and flow equations and gauge symmetries in particular. The third lecture deals with the flow equation in the background formalism which is particularly convenient for analytical computations of truncated flows. The fourth lecture concentrates on the transition from microscopic to macroscopic degrees of freedom; even though this is discussed here in the language and the context of QCD, the developed formalism is much more general and will be useful also for other systems.Comment: 60 pages, 14 figures, Lectures held at the 2006 ECT* School "Renormalization Group and Effective Field Theory Approaches to Many-Body Systems", Trento, Ital

The narrative self, distributed memory, and evocative objects

In this article, I outline various ways in which artifacts are interwoven with autobiographical memory systems and conceptualize what this implies for the self. I first sketch the narrative approach to the self, arguing that who we are as persons is essentially our (unfolding) life story, which, in turn, determines our present beliefs and desires, but also directs our future goals and actions. I then argue that our autobiographical memory is partly anchored in our embodied interactions with an ecology of artifacts in our environment. Lifelogs, photos, videos, journals, diaries, souvenirs, jewelry, books, works of art, and many other meaningful objects trigger and sometimes constitute emotionally-laden autobiographical memories. Autobiographical memory is thus distributed across embodied agents and various environmental structures. To defend this claim, I draw on and integrate distributed cognition theory and empirical research in human-technology interaction. Based on this, I conclude that the self is neither defined by psychological states realized by the brain nor by biological states realized by the organism, but should be seen as a distributed and relational construct

Functional renormalization group with a compactly supported smooth regulator function

The functional renormalization group equation with a compactly supported smooth (CSS) regulator function is considered. It is demonstrated that in an appropriate limit the CSS regulator recovers the optimized one and it has derivatives of all orders. The more generalized form of the CSS regulator is shown to reduce to all major type of regulator functions (exponential, power-law) in appropriate limits. The CSS regulator function is tested by studying the critical behavior of the bosonized two-dimensional quantum electrodynamics in the local potential approximation and the sine-Gordon scalar theory for d<2 dimensions beyond the local potential approximation. It is shown that a similar smoothing problem in nuclear physics has already been solved by introducing the so called Salamon-Vertse potential which can be related to the CSS regulator.Comment: JHEP style, 11 pages, 2 figures, proofs corrected, accepted for publication by JHE

High ultraviolet C resistance of marine Planctomycetes

Planctomycetes are bacteria with particular characteristics such as internal membrane systems encompassing intracellular compartments, proteinaceous cell walls, cell division by yeast-like budding and large genomes. These bacteria inhabit a wide range of habitats, including marine ecosystems, in which ultra-violet radiation has a potential harmful impact in living organisms. To evaluate the effect of ultra-violet C on the genome of several marine strains of Planctomycetes, we developed an easy and fast DNA diffusion assay in which the cell wall was degraded with papain, the wall-free cells were embedded in an agarose microgel and lysed. The presence of double strand breaks and unwinding by single strand breaks allow DNA diffusion, which is visible as a halo upon DNA staining. The number of cells presenting DNA diffusion correlated with the dose of ultra-violet C or hydrogen peroxide. From DNA damage and viability experiments, we found evidence indicating that some strains of Planctomycetes are significantly resistant to ultra-violet C radiation, showing lower sensitivity than the known resistant Arthrobacter sp. The more resistant strains were those phylogenetically closer to Rhodopirellula baltica, suggesting that these species are adapted to habitats under the influence of ultra-violet radiation. Our results provide evidence indicating that the mechanism of resistance involves DNA damage repair and/or other DNA ultra-violet C-protective mechanism.This research was supported by the European Regional Development Fund (ERDF) through the COMPETE-Operational Competitiveness Programme and national funds through FCT-Foundation for Science and Technology, under the projects Pest-C/BIA/UI4050/2011 and PEst-C/MAR/LA0015/2013. We are grateful to Catia Moreira for helping with the extraction of the pigments.info:eu-repo/semantics/publishedVersio

European integration assessed in the light of the 'rules vs. standards debate'

The interplay of various legal systems in the European Union (EU) has long triggered a debate on the tension between uniformity and diversity of Member States' (MS) laws. This debate takes place among European legal scholars and is also paralleled by economic scholars, e.g. in the ambit of the 'theory of federalism'. This paper takes an innovative perspective on the discrepancy between 'centralized' and 'decentralized' law-making in the EU by assessing it with the help of the rules versus standards debate. When should the EU legislator grant the national legislator leeway in the formulation of new laws and when should all be fixed ex ante at European level? The literature on the 'optimal shape of legal norms' shall be revisited in the light of law-making in the EU, centrally dealing with the question how much discretion shall be given to the national legislator; and under which circumstances. This paper enhances the established decisive factors for the choice of a rule or a standard in a national setting (complexity, volatility, judges' specialization and frequency of application) by two new crucial factors (switching costs and the benefit of uniformity in terms of information costs) in order to assess law-making policies at EU level

Reconciliation of halogen-induced ozone loss with the total-column ozone record

The observed depletion of the ozone layer from the 1980s onwards is attributed to halogen source gases emitted by human activities. However, the precision of this attribution is complicated by year-to-year variations in meteorology, that is, dynamical variability, and by changes in tropospheric ozone concentrations. As such, key aspects of the total-column ozone record, which combines changes in both tropospheric and stratospheric ozone, remain unexplained, such as the apparent absence of a decline in total-column ozone levels before 1980, and of any long-term decline in total-column ozone levels in the tropics. Here we use a chemistry–climate model to estimate changes in halogen-induced ozone loss between 1960 and 2010; the model is constrained by observed meteorology to remove the effects of dynamical variability, and driven by emissions of tropospheric ozone precursors to separate out changes in tropospheric ozone. We show that halogen-induced ozone loss closely followed stratospheric halogen loading over the studied period. Pronounced enhancements in ozone loss were apparent in both hemispheres following the volcanic eruptions of El Chichon and, in particular, Mount Pinatubo, which significantly enhanced stratospheric aerosol loads. We further show that approximately 40% of the long-term non-volcanic ozone loss occurred before 1980, and that long-term ozone loss also occurred in the tropical stratosphere. Finally, we show that halogen-induced ozone loss has declined by over 10% since stratospheric halogen loading peaked in the late 1990s, indicating that the recovery of the ozone layer is well underway

Action selection and action awareness

Human actions are often classified as either internally generated, or externally specified in response to environmental cues. These two modes of action selection have distinct neural bases, but few studies investigated how the mode of action selection affects the subjective experience of action. We measured the experience of action using the subjective compression of the interval between actions and their effects, known as ‘temporal binding’. Participants performed either a left or a right key press, either in response to a specific cue, or as they freely chose. Moreover, the time of each keypress could either be explicitly cued to occur in one of two designated time intervals, or participants freely chose in which interval to act. Each action was followed by a specific tone. Participants judged the time of their actions or the time of the tone. Temporal binding was found for both internally generated and for stimulus-based actions. However, the amount of binding depended on whether or not both the choice and the timing of action were selected in the same way. Stronger binding was observed when both action choice and action timing were internally generated or externally specified, compared to conditions where the two parameters were selected by different routes. Our result suggests that temporal action–effect binding depends on how actions are selected. Binding is strongest when actions result from a single mode of selection

Computing the effective action with the functional renormalization group

The \u201cexact\u201d or \u201cfunctional\u201d renormalization group equation describes the renormalization group flow of the effective average action \u393 k. The ordinary effective action \u393 0 can be obtained by integrating the flow equation from an ultraviolet scale k= \u39b down to k= 0. We give several examples of such calculations at one-loop, both in renormalizable and in effective field theories. We reproduce the four-point scattering amplitude in the case of a real scalar field theory with quartic potential and in the case of the pion chiral Lagrangian. In the case of gauge theories, we reproduce the vacuum polarization of QED and of Yang\u2013Mills theory. We also compute the two-point functions for scalars and gravitons in the effective field theory of scalar fields minimally coupled to gravity. \ua9 2016, The Author(s)