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We investigate the real-time dynamics of the chiral magnetic effect inquantum electrodynamics (QED) and quantum chromodynamics (QCD). We consider afield configuration of parallel (chromo)electric and (chromo)magnetic fieldswith a weak perpendicular electromagnetic magnetic field. The chiral magneticeffect induces an electromagnetic current along this perpendicular magneticfield, which we will compute using linear response theory. We discuss specificresults for a homogeneous sudden switch-on and a pulsed (chromo)electric fieldin a static and homogeneous (chromo)magnetic field. Our methodology can beeasily extended to more general situations. The results are useful forinvestigating the chiral magnetic effect with heavy ion collisions and withlasers that create strong electromagnetic fields. As a side result we obtainthe rate of chirality production for massive fermions in parallel electric andmagnetic fields that are static and homogeneous.

Dynamics of the Chiral Magnetic Effect in a weak magnetic field