Neutral Fermion Having Electric and Magnetic Moments in an External Electromagnetic Field

We show that in 2+1 dimensions, the Dirac equation for a neutral fermion possessing electric and magnetic dipole moments in an external electromagnetic field reduces to the Dirac equation for a “charged” fermion in a external field characterized by a certain “3-pseudo-vector potential.” The effective charge of the neutral fermion is determined by its dipole moments. The effects of coupling electric and magnetic moments of the neutral fermion to the external electromagnetic field seem to be inseparable in physical experiments of any type. We find an exact solution of the Dirac equation for a massive neutral fermion with electric and magnetic dipole moments in a external plane-wave electromagnetic field. We derive expressions for the fermionic vacuum current induced by neutral fermions in the presence of external electromagnetic fields.