The Heisenberg-Euler Effective Lagrangian and Nonlinear Quantum Effects in Electrodynamics

H. FALOMIR

Wallenberg Centre Stellenbosch - Sudáfrica

Workshop; Workshop on Nonlinear Effects in Quantum Electrodynamics; 2009

National Institute for Theoretical Physics

In these lectures, the Heisenber - Euler effective Lagrangian for QED is derived in two ways: employing the Schwinger's proper time approach and by means of zeta-function techniques. The required renormalizations and the pair creation rate are discussed. The weak-field asymptotic expansion of this Lagrangian is derived and, retaining the first terms, non-linear equations for the electromagnetic field are obtained. A perturbative expansion allows to get the first corrections to the electromagnetic field which, at large distances, can be interpreted as due to induced multipoles in the linear Maxwell theory.The case of a magnetized sphere immersed in an external electric field is considered, obtaining a dominant contribution which is equivalent to the field of an induced electric dipole which depends on the external field and the magnetic dipole moment. Since one expects this behavior of the field be robust, one can speculate about the behavior of a particle with spin in the presence of an (intense) electric field.