Renormalization of gauge fields using Hopf algebras

We describe the Hopf algebraic structure of Feynman graphs for non-abelian gauge theories, and prove compatibility of the so-called Slavnov-Taylor identities with the coproduct. When these identities are taken into account, the coproduct closes on the Green's functions, which thus generate a Hopf subalgebra.Comment: 16 pages, 1 figure; uses feynmp. To appear in "Recent Developments in Quantum Field Theory". Eds. B. Fauser, J. Tolksdorf and E. Zeidler. Birkhauser Verlag, Basel 200

On globally non-trivial almost-commutative manifolds

Within the framework of Connes' noncommutative geometry, we define and study globally non-trivial (or topologically non-trivial) almost-commutative manifolds. In particular, we focus on those almost-commutative manifolds that lead to a description of a (classical) gauge theory on the underlying base manifold. Such an almost-commutative manifold is described in terms of a 'principal module', which we build from a principal fibre bundle and a finite spectral triple. We also define the purely algebraic notion of 'gauge modules', and show that this yields a proper subclass of the principal modules. We describe how a principal module leads to the description of a gauge theory, and we provide two basic yet illustrative examples.Comment: 34 pages, minor revision

Particle Physics from Almost Commutative Spacetimes

Our aim in this review article is to present the applications of Connes' noncommutative geometry to elementary particle physics. Whereas the existing literature is mostly focused on a mathematical audience, in this article we introduce the ideas and concepts from noncommutative geometry using physicists' terminology, gearing towards the predictions that can be derived from the noncommutative description. Focusing on a light package of noncommutative geometry (so-called 'almost commutative manifolds'), we shall introduce in steps: electrodynamics, the electroweak model, culminating in the full Standard Model. We hope that our approach helps in understanding the role noncommutative geometry could play in describing particle physics models, eventually unifying them with Einstein's (geometrical) theory of gravity.Comment: 104 pages, 5 figures, version 2 (minor changes and some additional references

Exponential renormalization

Moving beyond the classical additive and multiplicative approaches, we present an "exponential" method for perturbative renormalization. Using Dyson's identity for Green's functions as well as the link between the Faa di Bruno Hopf algebra and the Hopf algebras of Feynman graphs, its relation to the composition of formal power series is analyzed. Eventually, we argue that the new method has several attractive features and encompasses the BPHZ method. The latter can be seen as a special case of the new procedure for renormalization scheme maps with the Rota-Baxter property. To our best knowledge, although very natural from group-theoretical and physical points of view, several ideas introduced in the present paper seem to be new (besides the exponential method, let us mention the notions of counterfactors and of order n bare coupling constants).Comment: revised version; accepted for publication in Annales Henri Poincar

Epidemiology of unintentional injuries in childhood:a population-based survey in general practice

This study aimed to assess the incidence of unintentional injuries presented in general practice, and to identify children at risk from experiencing an unintentional injury. We used the data of all 0-17-year-old children from a representative survey in 96 Dutch general practices in 2001. We computed incidence rates and multilevel multivariate regression analysis in different age strata and identified patient and family characteristics associated with an elevated injury risk. Nine thousand four hundred and eighty-four new injury episodes were identified from 105 353 new health problems presented in general practice, giving an overall incidence rate of 115 per 1000 person years (95% confidence interval [CI] = 113 to 118). Sex and residence in rural areas are strong predictors of injury in all age strata. Also, in children aged 0-4 years, a higher number of siblings is associated with elevated injury risk (≥3 siblings odds ratio [OR] = 1.57, 95% CI = 1.19 to 2.08) and in the 12-17-year-olds, ethnic background and socioeconomic class are associated with experiencing an injury (non-western children OR = 0.67, 95% CI = 0.54 to 0.81; low socioeconomic class OR = 1.39, 95% CI = 1.22 to 1.58). Unintentional injury is a significant health problem in children in general practice, accounting for 9% of all new health problems in children. In all age groups, boys in rural areas are especially at risk to experience an injury.</p

The noncommutative Lorentzian cylinder as an isospectral deformation

We present a new example of a finite-dimensional noncommutative manifold, namely the noncommutative cylinder. It is obtained by isospectral deformation of the canonical triple associated to the Euclidean cylinder. We discuss Connes' character formula for the cylinder. In the second part, we discuss noncommutative Lorentzian manifolds. Here, the definition of spectral triples involves Krein spaces and operators on Krein spaces. A central role is played by the admissible fundamental symmetries on the Krein space of square integrable sections of a spin bundle over a Lorentzian manifold. Finally, we discuss isospectral deformation of the Lorentzian cylinder and determine all admissible fundamental symmetries of the noncommutative cylinder.Comment: 30 page

Increasing incidence of skin disorders in children? A comparison between 1987 and 2001

BACKGROUND: The increasing proportion of skin diseases encountered in general practice represents a substantial part of morbidity in children. Only limited information is available about the frequency of specific skin diseases. We aimed to compare incidence rates of skin diseases in children in general practice between 1987 and 2001. METHODS: We used data on all children aged 0–17 years derived from two consecutive surveys performed in Dutch general practice in 1987 and 2001. Both surveys concerned a longitudinal registration of GP consultations over 12 months. Each disease episode was coded according to the International Classification of Primary Care. Incidence rates of separate skin diseases were calculated by dividing all new episodes for each distinct ICPC code by the average study population at risk. Data were stratified for socio-demographic characteristics. RESULTS: The incidence rate of all skin diseases combined in general practice decreased between 1987 and 2001. Among infants the incidence rate increased. Girls presented more skin diseases to the GP. In the southern part of the Netherlands children consulted their GP more often for skin diseases compared to the northern part. Children of non-Western immigrants presented relatively more skin diseases to the GP. In general practice incidence rates of specific skin diseases such as impetigo, dermatophytosis and atopic dermatitis increased in 2001, whereas warts, contact dermatitis and skin injuries decreased. CONCLUSION: The overall incidence rate of all skin diseases combined in general practice decreased whereas the incidence rates of bacterial, mycotic and atopic skin diseases increased

Non-Linear Algebra and Bogolubov's Recursion

Numerous examples are given of application of Bogolubov's forest formula to iterative solutions of various non-linear equations: one and the same formula describes everything, from ordinary quadratic equation to renormalization in quantum field theory.Comment: LaTex, 21 page