1,673 research outputs found

    A short elementary proof of Grothendieck s theorem on algebraic vectorbundles over the projective line

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    AbstractLet E be an algebraic (or holomorphic) vectorbundle over the Riemann sphere P1(C). Then Grothendieck proved that E splits into a sum of line bundles E = ⊕Li and the isomorphism classes of the Li are (up to order) uniquely determined by E. The Li in turn are classified by an integer (their Chern numbers) so that m-dimensional vectorbundles over P1C are classified by an m-tuple of integers Îș(E) = (Îș1(E),
,Îșm(E)), Îș1(E)≄⋯≄Îșm(E), Își(E)∈Z.In this short note we present a completely elementary proof of these facts which, as it turns out, works over any field k

    Representation of Sn S_ n and the geometry of linear systems

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    Representation of Sn S_ n and the geometry of linear systems

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    Charge asymmetry in W + jets production at the LHC

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    The charge asymmetry in W + jets production at the LHC can serve to calibrate the presence of New Physics contributions. We study the ratio {\sigma}(W^+ + n jets)/{\sigma}(W^- + n jets) in the Standard Model for n <= 4, paying particular attention to the uncertainty in the prediction from higher-order perturbative corrections and uncertainties in parton distribution functions. We show that these uncertainties are generally of order a few percent, making the experimental measurement of the charge asymmetry ratio a particularly useful diagnostic tool for New Physics contributions.Comment: 13 pages, 7 figures. Reference added. Slightly modified tex

    Representation of Quantum Field Theory by Elementary Quantum Information

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    In this paper is considered relativistic quantum field theory expressed by elementary units of quantum information as they are considered as fundamental entity of nature by Carl Friedrich von Weizsaecker. Through quantization of a Weyl spinor describing an elementary unit of quantum information and consisting of four real components one obtains four pairs of creation and annihilation operators acting in a tensor space of states containing many units of quantum information. There can be constructed position and momentum operators from the creation and annihilation operators and based on these operators the Poincare group can be represented in this abstract tensor space of quantum information. A general state in the tensor space can be mapped to a state in Minkowski space-time by using the position representation of the eigenstates of the occupation number operators which correspond to the eigenstates of the harmonic oscillator. This yields a description of relativistic quantum mechanics. Quantization of the coefficients of a general state in the tensor space leads to many particle theory and thus to quantum field theory.Comment: 7 page

    The resummation of inter-jet energy flow for gaps-between-jets processes at HERA

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    We calculate resummed perturbative predictions for gaps-between-jets processes and compare to HERA data. Our calculation of this non-global observable needs to include the effects of primary gluon emission (global logarithms) and secondary gluon emission (non-global logarithms) to be correct at the leading logarithm (LL) level. We include primary emission by calculating anomalous dimension matrices for the geometry of the specific event definitions and estimate the effect of non-global logarithms in the large NcN_c limit. The resulting predictions for energy flow observables are consistent with experimental data.Comment: 31 pages, 4 figures, 2 table

    Turbulent superfluid profiles in a counterflow channel

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    We have developed a two-dimensional model of quantised vortices in helium II moving under the influence of applied normal fluid and superfluid in a counterflow channel. We predict superfluid and vortex-line density profiles which could be experimentally tested using recently developed visualization techniques.Comment: 3 double figures, 9 page
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