Avoidance of a Landau pole by flat contributions in QED |
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Authors: | Lutz Klaczynski Dirk Kreimer |
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Institution: | 1. Department of Physics, Humboldt University Berlin, 12489 Berlin, Germany;2. Alexander von Humboldt Chair in Mathematical Physics, Humboldt University, Berlin 12489, Germany |
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Abstract: | We consider massless Quantum Electrodynamics in the momentum scheme and carry forward an approach based on Dyson–Schwinger equations to approximate both the β-function and the renormalized photon self-energy (Yeats, 2011). Starting from the Callan–Symanzik equation, we derive a renormalization group (RG) recursion identity which implies a non-linear ODE for the anomalous dimension and extract a sufficient but not necessary criterion for the existence of a Landau pole. This criterion implies a necessary condition for QED to have no such pole. Solving the differential equation exactly for a toy model case, we integrate the corresponding RG equation for the running coupling and find that even though the β-function entails a Landau pole it exhibits a flat contribution capable of decreasing its growth, in other cases possibly to the extent that such a pole is avoided altogether. Finally, by applying the recursion identity, we compute the photon propagator and investigate the effect of flat contributions on both spacelike and timelike photons. |
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Keywords: | Quantum electrodynamics β-function" target="_blank">gif" overflow="scroll">β-function Landau pole Callan&ndash Symanzik equation |
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