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

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

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

A comparison of three treatment strategies in recent onset non-systemic Juvenile Idiopathic Arthritis: Initial 3-months results of the BeSt for Kids-study

Background: Combination therapy with prednisone or etanercept may induce earlier and/or more improvement in disease activity in Disease Modifying Anti Rheumatic Drug (DMARD) naïve non-systemic Juvenile Idiopathic Arthritis (JIA) patients. Here we present three months clinical outcome of initial treatments of the BeSt-for-Kids study. Methods: Included patients were randomized to either: 1. initial DMARD-monotherapy (sulfasalazine (SSZ) or methotrexate (MTX)), 2. Initial MTX / prednisolone-bridging, 3. Initial combination MTX/etanercept. Percentage inactive disease, adjusted (a) ACR Pedi30, 50 and 70 and JADAS after 6 and 12 weeks of treatment (intention to treat analysis) and side effects are reported. Results: 94 patients (67% girls, 32 (arm 1), 32 (arm 2) and 30 (arm 3) with median (InterQuartileRange) age of 9.1 (4.7-12.9) years were included. 38% were ANA positive, 10 had oligo-articular disease, 68 polyarticular JIA and 16 psoriatic arthritis. Baseline median (IQR) ACRpedi-scores: VAS physician 49 (40-58) mm, VAS patient 54 (37-70) mm, ESR 6.5 (2-14.8)mm/hr, active joint count 8 (5-12), limited joint count 3 (1-5), CHAQ score 0.88 (0.63-1.5). In arm 1, 17 started with MTX, 15 with SSZ. After 3 months, aACR Pedi 50 was reached by 10/32 (31%), 12/32(38%) and 16/30 (53%) (p = 0.19) and aACR Pedi 70 was reached by 8/32 (25%), 6/32(19%) and 14/30(47%) in arms 1-3 (p = 0.04). Toxicity was similar. Few serious adverse events were reported. Conclusion: After 3 months of treatment in a randomized trial, patients with recent-onset JIA achieved significantly more clinical improvement (aACRPedi70) on initial combination therapy with MTX / etanercept than on initial MTX or SSZ monotherapy. Trial registration:NTR1574. Registered 3 December 2008

A survey of spectral models of gravity coupled to matter

This is a survey of the historical development of the Spectral Standard Model and beyond, starting with the ground breaking paper of Alain Connes in 1988 where he observed that there is a link between Higgs fields and finite noncommutative spaces. We present the important contributions that helped in the search and identification of the noncommutative space that characterizes the fine structure of space-time. The nature and properties of the noncommutative space are arrived at by independent routes and show the uniqueness of the Spectral Standard Model at low energies and the Pati-Salam unification model at high energies.Comment: An appendix is added to include scalar potential analysis for a Pati-Salam model. 58 Page

Motives and periods in Bianchi IX gravity models

In this paper we show that the heat coefficients of the Dirac-Laplacian of SU(2)-invariant Bianchi IX metrics are periods of motives of complements in affine spaces of unions of quadrics and hyperplanes

International consensus on the most useful physical examination tests used by physiotherapists for patients with headache: A Delphi study

Background: A wide range of physical tests have been published for use in the assessment of musculoskeletal dysfunction in patients with headache. Which tests are used depends on a physiotherapist's clinical and scientific background as there is little guidance on the most clinically useful tests. Objectives: To identify which physical examination tests international experts in physiotherapy consider the most clinically useful for the assessment of patients with headache. Design/methods: Delphi survey with pre-specified procedures based on a systematic search of the literature for physical examination tests proposed for the assessment of musculoskeletal dysfunction in patients with headache. Results: Seventeen experts completed all three rounds of the survey. Fifteen tests were included in round one with eleven additional tests suggested by the experts. Finally eleven physical examination tests were considered clinically useful: manual joint palpation, the cranio-cervical flexion test, the cervical flexion-rotation test, active range of cervical movement, head forward position, trigger point palpation, muscle tests of the shoulder girdle, passive physiological intervertebral movements, reproduction and resolution of headache symptoms, screening of the thoracic spine, and combined movement tests. Conclusions: Eleven tests are suggested as a minimum standard for the physical examination of musculoskeletal dysfunctions in patients with headache