119600095
QFT, RG, and all that, for mathematicians, in eleven pages
We present a quick introduction to quantum field theory and Wilson's theory of the renormalization group from the point of view of mathematical analysis. The presentation is geared primarily towards a probability theory, harmonic analysis and dynamical systems theory audience.
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.
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.
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.
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.
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.
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.