4 resultados para Singularities in Feynman propagators

em Universidade do Minho


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Dissertação de mestrado em Design de Comunicação de Moda

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This chapter describes the how the vector of coordinates are defined in the formulation of spatial multibody systems. For this purpose, the translational motion is described in terms of Cartesian coordinates, while rotational motion is specified using the technique of Euler parameters. This approach avoids the computational difficulties associated with the singularities in the case of using Euler angles or Bryant angles. Moreover, the formulation of the velocities vector and accelerations vector is presented and analyzed here. These two sets of vectors are defined in terms of translational and rotational coordinates.

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The transverse polarization of Λ and Λ¯ hyperons produced in proton--proton collisions at a center-of-mass energy of 7 TeV is measured. The analysis uses 760 μb−1 of minimum bias data collected by the ATLAS detector at the LHC in the year 2010. The measured transverse polarization averaged over Feynman xF from 5×10−5 to 0.01 and transverse momentum pT from 0.8 to 15 GeV is −0.010±0.005(stat)±0.004(syst) for Λ and 0.002±0.006(stat)±0.004(syst) for Λ¯. It is also measured as a function of xF and pT, but no significant dependence on these variables is observed. Prior to this measurement, the polarization was measured at fixed-target experiments with center-of-mass energies up to about 40 GeV. The ATLAS results are compatible with the extrapolation of a fit from previous measurements to the xF range covered by this mesurement.

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We study the longitudinal and transverse spin dynamical structure factors of the spin-1/2 XXX chain at finite magnetic field h, focusing in particular on the singularities at excitation energies in the vicinity of the lower thresholds. While the static properties of the model can be studied within a Fermi-liquid like description in terms of pseudoparticles, our derivation of the dynamical properties relies on the introduction of a form of the ‘pseudofermion dynamical theory’ (PDT) of the 1D Hubbard model suitably modified for the spin-only XXX chain and other models with two pseudoparticle Fermi points. Specifically, we derive the exact momentum and spin-density dependences of the exponents ζτ(k) controlling the singularities for both the longitudinal  and transverse (τ = t) dynamical structure factors for the whole momentum range  , in the thermodynamic limit. This requires the numerical solution of the integral equations that define the phase shifts in these exponents expressions. We discuss the relation to neutron scattering and suggest new experiments on spin-chain compounds using a carefully oriented crystal to test our predictions.