Asymptotically free four-fermion interactions and electroweak symmetry breaking

We investigate the fermions of the standard model without a Higgs scalar. Instead, we consider a non-local four-quark interaction in the tensor channel which is characterized by a single dimensionless coupling $f$. Quantization leads to a consistent perturbative expansion for small $f$. The running of $f$ is asymptotically free and therefore induces a non-perturbative scale $\Lambda_{ch}$, in analogy to the strong interactions. We argue that spontaneous electroweak symmetry breaking is triggered at a scale where $f$ grows large and find the top quark mass of the order of $\Lambda_{ch}$. We also present a first estimate of the effective Yukawa coupling of a composite Higgs scalar to the top quark, as well as the associated mass ratio between the top quark and the W boson.Comment: 24 page

Comparison of Boltzmann Equations with Quantum Dynamics for Scalar Fields

Boltzmann equations are often used to study the thermal evolution of particle reaction networks. Prominent examples are the computation of the baryon asymmetry of the universe and the evolution of the quark-gluon plasma after relativistic heavy ion collisions. However, Boltzmann equations are only a classical approximation of the quantum thermalization process which is described by the so-called Kadanoff-Baym equations. This raises the question how reliable Boltzmann equations are as approximations to the full Kadanoff-Baym equations. Therefore, we present in this paper a detailed comparison between the Kadanoff-Baym and Boltzmann equations in the framework of a scalar Phi^4 quantum field theory in 3+1 space-time dimensions. The obtained numerical solutions reveal significant discrepancies in the results predicted by both types of equations. Apart from quantitative discrepancies, on a qualitative level the universality respected by the Kadanoff-Baym equations is severely restricted in the case of Boltzmann equations. Furthermore, the Kadanoff-Baym equations strongly separate the time scales between kinetic and chemical equilibration. This separation of time scales is absent for the Boltzmann equation.Comment: text and figures revised, references added, results unchanged, 21 pages, 10 figures, published in Phys. Rev. D73 (2006) 12500

Comparison of Boltzmann Kinetics with Quantum Dynamics for a Chiral Yukawa Model Far From Equilibrium

Boltzmann equations are often used to describe the non-equilibrium time-evolution of many-body systems in particle physics. Prominent examples are the computation of the baryon asymmetry of the universe and the evolution of the quark-gluon plasma after a relativistic heavy ion collision. However, Boltzmann equations are only a classical approximation of the quantum thermalization process, which is described by so-called Kadanoff-Baym equations. This raises the question how reliable Boltzmann equations are as approximations to the complete Kadanoff-Baym equations. Therefore, we present in this article a detailed comparison of Boltzmann and Kadanoff-Baym equations in the framework of a chirally invariant Yukawa-type quantum field theory including fermions and scalars. The obtained numerical results reveal significant differences between both types of equations. Apart from quantitative differences, on a qualitative level the late-time universality respected by Kadanoff-Baym equations is severely restricted in the case of Boltzmann equations. Furthermore, Kadanoff-Baym equations strongly separate the time scales between kinetic and chemical equilibration. In contrast to this standard Boltzmann equations cannot describe the process of quantum-chemical equilibration, and consequently also cannot feature the above separation of time scales.Comment: 17 pages, 8 figures, REVTeX

Exposure to Inhalable, Respirable, and Ultrafine Particles in Welding Fume

This investigation aims to explore determinants of exposure to particle size-specific welding fume. Area sampling of ultrafine particles (UFP) was performed at 33 worksites in parallel with the collection of respirable particles. Personal sampling of respirable and inhalable particles was carried out in the breathing zone of 241 welders. Median mass concentrations were 2.48 mg m−3 for inhalable and 1.29 mg m−3 for respirable particles when excluding 26 users of powered air-purifying respirators (PAPRs). Mass concentrations were highest when flux-cored arc welding (FCAW) with gas was applied (median of inhalable particles: 11.6 mg m−3). Measurements of particles were frequently below the limit of detection (LOD), especially inside PAPRs or during tungsten inert gas welding (TIG). However, TIG generated a high number of small particles, including UFP. We imputed measurements <LOD from the regression equation with manganese to estimate determinants of the exposure to welding fume. Concentrations were mainly predicted by the welding process and were significantly higher when local exhaust ventilation (LEV) was inefficient or when welding was performed in confined spaces. Substitution of high-emission techniques like FCAW, efficient LEV, and using PAPRs where applicable can reduce exposure to welding fume. However, harmonizing the different exposure metrics for UFP (as particle counts) and for the respirable or inhalable fraction of the welding fume (expressed as their mass) remains challenging

Algorithmic derivation of functional renormalization group equations and Dyson-Schwinger equations

We present the Mathematica application DoFun which allows to derive Dyson-Schwinger equations and renormalization group flow equations for n-point functions in a simple manner. DoFun offers several tools which considerably simplify the derivation of these equations from a given physical action. We discuss the application of DoFun by means of two different types of quantum field theories, namely a bosonic O(N) theory and the Gross-Neveu model.Comment: 40 pages, 12 figs.; corresponds to published versio

A Minimal Length from the Cutoff Modes in Asymptotically Safe Quantum Gravity

Within asymptotically safe Quantum Einstein Gravity (QEG), the quantum 4-sphere is discussed as a specific example of a fractal spacetime manifold. The relation between the infrared cutoff built into the effective average action and the corresponding coarse graining scale is investigated. Analyzing the properties of the pertinent cutoff modes, the possibility that QEG generates a minimal length scale dynamically is explored. While there exists no minimal proper length, the QEG sphere appears to be "fuzzy" in the sense that there is a minimal angular separation below which two points cannot be resolved by the cutoff modes.Comment: 26 pages, 1 figur

CrasyDSE: A framework for solving Dyson-Schwinger equations

Dyson-Schwinger equations are important tools for non-perturbative analyses of quantum field theories. For example, they are very useful for investigations in quantum chromodynamics and related theories. However, sometimes progress is impeded by the complexity of the equations. Thus automatizing parts of the calculations will certainly be helpful in future investigations. In this article we present a framework for such an automatization based on a C++ code that can deal with a large number of Green functions. Since also the creation of the expressions for the integrals of the Dyson-Schwinger equations needs to be automatized, we defer this task to a Mathematica notebook. We illustrate the complete workflow with an example from Yang-Mills theory coupled to a fundamental scalar field that has been investigated recently. As a second example we calculate the propagators of pure Yang-Mills theory. Our code can serve as a basis for many further investigations where the equations are too complicated to tackle by hand. It also can easily be combined with DoFun, a program for the derivation of Dyson-Schwinger equations.Comment: 39 pages, 8 tables, 9 figs.; program version 1.1.0; added summaries on main functions and more details on syntax and auxiliary functions; source code available at http://theorie.ikp.physik.tu-darmstadt.de/~mqh/CrasyDSE

Scale-dependent metric and causal structures in Quantum Einstein Gravity

Within the asymptotic safety scenario for gravity various conceptual issues related to the scale dependence of the metric are analyzed. The running effective field equations implied by the effective average action of Quantum Einstein Gravity (QEG) and the resulting families of resolution dependent metrics are discussed. The status of scale dependent vs. scale independent diffeomorphisms is clarified, and the difference between isometries implemented by scale dependent and independent Killing vectors is explained. A concept of scale dependent causality is proposed and illustrated by various simple examples. The possibility of assigning an "intrinsic length" to objects in a QEG spacetime is also discussed.Comment: 52 page