16110261
A physicist's proof of the Lagrange?Good multivariable inversion formula
We provide a new proof, inspired by quantum field theory, of the Lagrange--Good multivariable inversion formula.
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.
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.
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.
17794922
Trees, forests and jungles: a botanical garden for cluster expansions
Combinatoric formulas for cluster expansions have been improved many times over the years. Here we develop some new combinatoric proofs and extensions of the tree formulas of Brydges and Kennedy, and test them on a series of pedagogical examples.
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.