Non-Uniqueness of Quantized Yang-Mills Theories

We consider quantized Yang-Mills theories in the framework of causal perturbation theory which goes back to Epstein and Glaser. In this approach gauge invariance is expressed by a simple commutator relation for the S-matrix. The most general coupling which is gauge invariant in first order contains a two-parametric ambiguity in the ghost sector - a divergence- and a coboundary-coupling may be added. We prove (not completely) that the higher orders with these two additional couplings are gauge invariant, too. Moreover we show that the ambiguities of the n-point distributions restricted to the physical subspace are only a sum of divergences (in the sense of vector analysis). It turns out that the theory without divergence- and coboundary-coupling is the most simple one in a quite technical sense. The proofs for the n-point distributions containing coboundary-couplings are given up to third or fourth order only, whereas the statements about the divergence-coupling are proven in all orders.Comment: 22 pages. The paper is written in TEX. The necessary macros are include

On the Influence of Eccentricities on Flux Linkages of Permanent Magnet Synchronous Machines

The noise behavior of electrical machines is influenced by tolerances. Eccentricities in particular lead to poorer noise behavior. However, the measurement of NVH quantities is usually very complex. Therefore, it is of interest to be able to detect such tolerances also by other measurands. In this paper, the influence of eccentricities on the flux linkages is investigated. For this purpose, detailed investigations were carried out using FEA. In a further step, these are compared with the results obtained from a test rig measurement. Prior to this, a methodology is presented with which the angle-dependent flux linkages can be determined. It is shown that eccentricities cause only slight changes in the harmonic components of the flux linkages. Due to the symmetry properties of the investigated machine, the changes in the flux linkage caused by the different air gap lengths cancel each other out. This could also be confirmed in the experiment

Representation of acoustic communication signals by insect auditory receptor neurons

Despite their simple auditory systems, some insect species recognize certain temporal aspects of acoustic stimuli with an acuity equal to that of vertebrates; however, the underlying neural mechanisms and coding schemes are only partially understood. In this study, we analyze the response characteristics of the peripheral auditory system of grasshoppers with special emphasis on the representation of species-specific communication signals. We use both natural calling songs and artificial random stimuli designed to focus on two low-order statistical properties of the songs: their typical time scales and the distribution of their modulation amplitudes. Based on stimulus reconstruction techniques and quantified within an information-theoretic framework, our data show that artificial stimuli with typical time scales of >40 msec can be read from single spike trains with high accuracy. Faster stimulus variations can be reconstructed only for behaviorally relevant amplitude distributions. The highest rates of information transmission (180 bits/sec) and the highest coding efficiencies (40%) are obtained for stimuli that capture both the time scales and amplitude distributions of natural songs. Use of multiple spike trains significantly improves the reconstruction of stimuli that vary on time scales <40 msec or feature amplitude distributions as occur when several grasshopper songs overlap. Signal-to-noise ratios obtained from the reconstructions of natural songs do not exceed those obtained from artificial stimuli with the same low-order statistical properties. We conclude that auditory receptor neurons are optimized to extract both the time scales and the amplitude distribution of natural songs. They are not optimized, however, to extract higher-order statistical properties of the song-specific rhythmic patterns

On Gauge Invariance and Spontaneous Symmetry Breaking

We show how the widely used concept of spontaneous symmetry breaking can be explained in causal perturbation theory by introducing a perturbative version of quantum gauge invariance. Perturbative gauge invariance, formulated exclusively by means of asymptotic fields, is discussed for the simple example of Abelian U(1) gauge theory (Abelian Higgs model). Our findings are relevant for the electroweak theory, as pointed out elsewhere.Comment: 13 pages, latex, no figure

The Epstein-Glaser approach to pQFT: graphs and Hopf algebras

The paper aims at investigating perturbative quantum field theory (pQFT) in the approach of Epstein and Glaser (EG) and, in particular, its formulation in the language of graphs and Hopf algebras (HAs). Various HAs are encountered, each one associated with a special combination of physical concepts such as normalization, localization, pseudo-unitarity, causality and an associated regularization, and renormalization. The algebraic structures, representing the perturbative expansion of the S-matrix, are imposed on the operator-valued distributions which are equipped with appropriate graph indices. Translation invariance ensures the algebras to be analytically well-defined and graded total symmetry allows to formulate bialgebras. The algebraic results are given embedded in the physical framework, which covers the two recent EG versions by Fredenhagen and Scharf that differ with respect to the concrete recursive implementation of causality. Besides, the ultraviolet divergences occuring in Feynman's representation are mathematically reasoned. As a final result, the change of the renormalization scheme in the EG framework is modeled via a HA which can be seen as the EG-analog of Kreimer's HA.Comment: 52 pages, 5 figure

Affective touch and attachment style modulate pain: a laser-evoked potentials study

Affective touch and cutaneous pain are two sub-modalities of interoception with contrasting affective qualities (pleasantness/unpleasantness) and social meanings (care/harm), yet their direct relationship has not been investigated. In 50 women, taking into account individual attachment styles, we assessed the role of affective touch and particularly the contribution of the C tactile (CT) system in subjective and electrophysiological responses to noxious skin stimulation, namely N1 and N2-P2 laser-evoked potentials. When pleasant, slow (versus fast) velocity touch was administered to the (non-CT-containing) palm of the hand, higher attachment anxiety predicted increased subjective pain ratings, in the same direction as changes in N2 amplitude. By contrast, when pleasant touch was administered to CT-containing skin of the arm, higher attachment anxiety predicted attenuated N1 and N2 amplitudes. Higher attachment avoidance predicted opposite results. Thus, CT-based affective touch can modulate pain in early and late processing stages (N1 and N2 components), with the direction of effects depending on attachment style. Affective touch not involving the CT system seems to affect predominately the conscious perception of pain, possibly reflecting socio-cognitive factors further up the neurocognitive hierarchy. Affective touch may thus convey information about available social resources and gate pain responses depending on individual expectations of social support

Fluctuations and differential contraction during regeneration of Hydra vulgaris tissue toroids

We studied regenerating bilayered tissue toroids dissected from Hydra vulgaris polyps and relate our macroscopic observations to the dynamics of force-generating mesoscopic cytoskeletal structures. Tissue fragments undergo a specific toroid-spheroid folding process leading to complete regeneration towards a new organism. The time scale of folding is too fast for biochemical signalling or morphogenetic gradients which forced us to assume purely mechanical self-organization. The initial pattern selection dynamics was studied by embedding toroids into hydro-gels allowing us to observe the deformation modes over longer periods of time. We found increasing mechanical fluctuations which break the toroidal symmetry and discuss the evolution of their power spectra for various gel stiffnesses. Our observations are related to single cell studies which explain the mechanical feasibility of the folding process. In addition, we observed switching of cells from a tissue bound to a migrating state after folding failure as well as in tissue injury. We found a supra-cellular actin ring assembled along the toroid's inner edge. Its contraction can lead to the observed folding dynamics as we could confirm by finite element simulations. This actin ring in the inner cell layer is assembled by myosin- driven length fluctuations of supra-cellular {\alpha}-actin structures (myonemes) in the outer cell-layer.Comment: 19 pages and 8 figures, submitted to New Journal of Physic

Modeling human-water-systems: towards a comprehensive and spatially distributed assessment of co-evolutions for river basins in Central Europe

In the context of river basin and flood risk management there is a growing need to improve the understanding of and the feedbacks between the driving forces “climate and socio-economy” and water systems. We make use of a variety of data resources to illustrate interrelationships between different constituents of the human-water-systems. Taking water storage for energy production as an example we present a first analysis on the co-evolution of socio-economic and hydrological indicators. The findings will serve as for the development of conceptual, but fully coupled socio-hydrological models for selected sectors and regions. These models will be used to generate integrated scenarios of the climate and socio-economic change

Massive Vector Mesons and Gauge Theory

We show that the requirements of renormalizability and physical consistency imposed on perturbative interactions of massive vector mesons fix the theory essentially uniquely. In particular physical consistency demands the presence of at least one additional physical degree of freedom which was not part of the originally required physical particle content. In its simplest realization (probably the only one) these are scalar fields as envisaged by Higgs but in the present formulation without the ``symmetry-breaking Higgs condensate''. The final result agrees precisely with the usual quantization of a classical gauge theory by means of the Higgs mechanism. Our method proves an old conjecture of Cornwall, Levin and Tiktopoulos stating that the renormalization and consistency requirements of spin=1 particles lead to the gauge theory structure (i.e. a kind of inverse of 't Hooft's famous renormalizability proof in quantized gauge theories) which was based on the on-shell unitarity of the $S$-matrix. We also speculate on a possible future ghostfree formulation which avoids ''field coordinates'' altogether and is expected to reconcile the on-shell S-matrix point of view with the off-shell field theory structure.Comment: 53 pages, version to appear in J. Phys.