92,645 research outputs found

    Checking the transverse Ward-Takahashi relation at one loop order in 4-dimensions

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    Some time ago Takahashi derived so called {\it transverse} relations relating Green's functions of different orders to complement the well-known Ward-Green-Takahashi identities of gauge theories by considering wedge rather than inner products. These transverse relations have the potential to determine the full fermion-boson vertex in terms of the renormalization functions of the fermion propagator. He & Yu have given an indicative proof at one-loop level in 4-dimensions. However, their construct involves the 4th rank Levi-Civita tensor defined only unambiguously in 4-dimensions exactly where the loop integrals diverge. Consequently, here we explicitly check the proposed transverse Ward-Takahashi relation holds at one loop order in dd-dimensions, with d=4+ϵd=4+\epsilon.Comment: 20 pages, 3 figures This version corrects and clarifies the previous result. This version has been submitted for publicatio

    Random Time-Scale Invariant Diffusion and Transport Coefficients

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    Single particle tracking of mRNA molecules and lipid granules in living cells shows that the time averaged mean squared displacement δ2‾\overline{\delta^2} of individual particles remains a random variable while indicating that the particle motion is subdiffusive. We investigate this type of ergodicity breaking within the continuous time random walk model and show that δ2‾\overline{\delta^2} differs from the corresponding ensemble average. In particular we derive the distribution for the fluctuations of the random variable δ2‾\overline{\delta^2}. Similarly we quantify the response to a constant external field, revealing a generalization of the Einstein relation. Consequences for the interpretation of single molecule tracking data are discussed.Comment: 4 pages, 4 figures.Article accompanied by a PRL Viewpoint in Physics1, 8 (2008
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