Avoidance of a Landau pole by flat contributions in QED

作者：Klaczynski Lutz^*; Kreimer Dirk

来源：Annals of Physics, 2014, 344: 213-231.

DOI：10.1016/j.aop.2014.02.019

• Quantum electrodynamics
• beta-function
• Landau pole
• Callan-Symanzik equation

We consider massless Quantum Electrodynamics in the momentum scheme and carry forward an approach based on Dyson-Schwinger equations to approximate both the beta-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 beta-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.

• 出版日期2014-5