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.
118449829
Rigorous quantum field theory functional integrals over the p-adics: research announcement
In this short note we announce the construction of scale invariant non-Gaussian generalized stochastic processes over three dimensional p-adic space. The construction includes that of the associated squared field and our result shows this squared field has a dynamically generated anomalous dimension which rigorously confirms a prediction made more than forty years ago, in an essentially identical situation, by Kenneth G. Wilson. We also prove a mild form of universality for the model under consideration.
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.
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
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.