118707104
Explicit Fermionic Tree Expansions
We express connected Fermionic Green's functions in terms of two totally explicit tree formulas. The simplest and most symmetric formula, the Brydges–Kennedy formula is compatible with Gram's inequality. The second one, the rooted formula of Abdesselam and Rivasseau, respects even better the antisymmetric structure of determinants, and allows the direct comparison of rows and columns which correspond to the mathematical implementation in Grassmann integrals of the Pauli principle. To illustrate the power of these formulas, we give a ‘three lines proof’ that the radius of convergence of the Gross–Neveu theory with cutoff is independent of the number of colors, using either one or the other of these formulas.
119175938
Feynman Diagrams in Algebraic Combinatorics
We show, in great detail, how the perturbative tools of quantum field theory allow one to rigorously obtain: a ``categorified'' Faa di Bruno type formula for multiple composition, an explicit formula for reversion and a proof of Lagrange-Good inversion, all in the setting of multivariable power series. We took great pains to offer a self-contained presentation that, we hope, will provide any mathematician who wishes, an easy access to the wonderland of quantum field theory.
18388560
A Complete Renormalization Group Trajectory Between Two Fixed Points
We give a rigorous nonperturbative construction of a massless discrete trajectory for Wilson’s exact renormalization group. The model is a three dimensional Euclidean field theory with a modified free propagator. The trajectory realizes the mean field to critical crossover from the ultraviolet Gaussian fixed point to an analog recently constructed by Brydges, Mitter and Scoppola of the Wilson-Fisher nontrivial fixed point.
119161955
The Ground State Energy of the Massless Spin-Boson Model
We provide an explicit combinatorial expansion for the ground state energy of the massless spin-Boson model as a power series in the coupling parameter. Our method uses the technique of cluster expansion in constructive quantum field theory and takes as a starting point the functional integral representation and its reduction to an Ising model on the real line with long range interactions. We prove the analyticity of our expansion and provide an explicit lower bound on the radius of convergence. We do not need multiscale nor renormalization group analysis. A connection to the loop-erased random walk is indicated.
15648354
Brill-Gordan loci, transvectants and an analogue of the Foulkes conjecture
The hypersurfaces of degree d in the projective space Pn correspond to points of PN, where N=(n+dd)−1. Now assume d=2e is even, and let X(n,d)⊆PN denote the subvariety of two e-fold hyperplanes. We exhibit an upper bound on the Castelnuovo regularity of the ideal of X(n,d), and show that this variety is r-normal for r⩾2. The latter result is representation-theoretic, and says that a certain GLn+1-equivariant morphism 
Sr(S2e(Cn+1))→S2(Sre(Cn+1)) 
is surjective for r⩾2; a statement which is reminiscent of the Foulkes–Howe conjecture. For its proof, we reduce the statement to the case n=1, and then show that certain transvectants of binary forms are nonzero. The latter part uses explicit calculations with Feynman diagrams and hypergeometric series. For ternary quartics and binary d-ics, we give explicit generators for the defining ideal of X(n,d) expressed in the language of classical invariant theory.
17032794
Bosonic Monocluster Expansion
Abstract: We compute Green's functions of a Bosonic field theory with cutoffs by means of a “minimal” expansion which in a single move, interpolating a generalized propagator, performs the usual tasks of the cluster and Mayer expansion. In this way it allows a direct construction of the infinite volume or thermodynamic limit and it brings constructive Bosonic expansions closer to constructive Fermionic expansions and to perturbation theory.
9626406
The detector control system for the ATLAS semiconductor tracker assembly phase
The ATLAS Semiconductor tracker (SCT) consists of 4088 silicon microstrip modules, with a total of 6.3 million readout channels. These are arranged into 4 concentric barrel layers and 2 endcaps of 9 disks each. The coherent and safe operation of the SCT during commissioning and subsequent operation is an essential task of the Detector Control System (DCS). The main building blocks of the SCT DCS, the cooling system, the power supplies and the environmental system, are described. First results from DCS testing are presented.
170390949
Recherche de production resonante de sleptons au run I de D0 & identification et mesure des electrons au run II
Une recherche de production resonante de particules supersymetrique (smuon et sneutrino du muon) est presentee. Le cadre theorique de cette etude est le modele msugra, ou on considere cinq parametres libres : m 0, m 1 / 2, tan, a 0, sign(), avec r-parite violee (un parametre). Deux methodes d'analyse ont ete appliquees : l'analyse sequentielle consideree comme une methode traditionnelle et l'analyse par reseau de neurones qui est de plus en plus utilisee comme outil en physique des particules. Notre etude est basee sur les donnees du run i de l'experience d aupres du tevatron a fermilab (usa). La luminosite consideree est de 94pb 1. Aucun exces par rapport aux predictions du modele standard n'a ete observe, on interprete par consequent ce resultat en termes de limites sur les parametres du modele utilise. Des contours d'exclusion a 95% de niveau de confiance dans le plan (m 0, m 1 / 2) sont donnes. Des valeurs de m 0 et m 1 / 2 jusqu'a 230 gev et 260 gev sont exclues pour une constante de couplage 2 1 1 = 0. 09, tan = 2, sign () = 1 et a 0 = 0. On peut aussi interpreter ce resultat par des contours d'exclusion dans les plans des masses, (m , m x 10) par exemple, ou est le sneutrino du muon et x 0 1 est le neutralino le plus leger. Des masses (relatives) du et x 0 1 de 280 gev et 112gev sont exclues a 95% de niveau de confiance. Cette meme analyse peut etre refaite sur les donnees du run ii qui beneficie d'une plus grande luminosite instantanee (5. 2 10 3 2 cm 2s 1 au run ii contre 0. 86 10 3 2 cm 2s 1 au run i) et une plus grande energie dans le centre de masse (2tev contre un 1. 8tev au run i). Cela permettra de restreindre d'avantage les parametres de msugra et comme consequence les masses des particules supersymetriques. Une autre partie de ce travail traite de l'identification de l'electron au run ii qui est tres importante pour la recherche d'une nouvelle physique. Plusieurs outils sont utilises pour une telle fin. Particulierement nous avons etudie les performances de la matrice de covariance (matrice h).
120192224
Measurements of sigma(e^+ e^- -> Upsilon(nS)pi^+pi^-) and sigma(e^+ e^- -> b bbar) in the Upsilon(10860) and Upsilon(11020) resonance regions