Euler-Heisenberg Lagrangian to all orders in the magnetic field and the Chiral Magnetic Effect

摘要

In high energy heavy ion collisions as well as in astrophysical objects likemagnetars extreme magnetic field strengths are reached. Thus, there exists aneed to calculate divers QED processes to all orders in the magnetic field. Wecalculate the vacuum polarization graph in second order of the electric fieldand all orders of the magnetic field resulting in a generalization of theEuler-Heisenberg Lagrangian. We perform the calculation in the effectiveLagrangian approach of J. Schwinger as well as using modified Feynman rules. Wefind that both approaches give the same results provided that the differentfinite renormalization terms are taken into account. Our results imply that anyquantitative explanation of the recently proposed Chiral Magnetic Effect has totake 'Strong QED' effects into account, because these corrections are huge.