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.
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.
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.
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.
14876309
The bipartite Brill-Gordan locus and angular momentum
AbstractGiven integers n,d,e with $1 \leqslant e < \frac{d}{2},$ let $X \subseteq {\Bbb P}^{\binom{d+n}{d}-1}$ denote the locus of degree d hypersurfaces in ${\Bbb P}^n$ which are supported on two hyperplanes with multiplicities d-e and e. Thus X is the Brill-Gordan locus associated to the partition (d-e,e). The main result of this paper is an exact determination of the Castelnuovo regularity of the ideal of X. Moreover, we show that X is r-normal for $r \geqslant 3.$ In the case of binary forms (i.e., for n = 1) we give an invariant-theoretic description of the ideal generators and, furthermore, exhibit a set of two covariants which define this locus set-theoretically. In addition to the standard cohomological tools in algebraic geometry, the proof crucially relies on the nonvanishing of certain 3j-symbols from the quantum theory of
angular momentum.
5900178
An Explicit Large Versus Small Field Multiscale Cluster Expansion
We introduce a new type of cluster expansion which generalizes a previous formula of Brydges and Kennedy. The method is especially suited for performing a phase-space multiscale expansion in a just renormalizable theory, and allows the writing of explicit non-perturbative formulas for the Schwinger functions. The procedure is quite model independent, but for simplicity we chose the infrared $\ph^4_4$ model as a testing ground. We used also a large field versus small field expansion. The polymer amplitudes, corresponding to graphs without almost local two and for point functions, are shown to satisfy the polymer bound.
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.
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
110275378
The control and monitoring system for the ATLAS semi-conductor tracker
Abstract The ATLAS Semi-Conductor Tracker (SCT) will be made of 4088 silicon modules mounted on four barrel supports and eighteen end cap disks. At present module production has started in different sites all around the world. The assembly of the modules into the support structures is taking place at three different macro-assembly sites. To allow for the safety operation of the detector a Detector Control System (DCS) is being developed at CERN that will be close to the final ATLAS configuration. The DCS will control and monitor the power supply provided to the modules, the cooling system and the environmental variables. This paper will give an overview of the system required to operate and readout large-scale silicon detectors.