Neutrinos, Electrons and Muons in Electromagnetic Fields and Matter: The Method of Exact Solutions

We present a powerful method for exploring various processes in the presence of strong external fields and matter. The method implies utilization of the exact solutions of the modified Dirac equations which contain the effective potentials accounting for the influences of external electromagnetic fields and matter on particles. We briefly discuss the basics of the method and its applications to studies of different processes, including a recently proposed new mechanism of radiation by neutrinos and electrons moving in matter (the spin light of the neutrino and electron). In view of a recent "prediction" of an order-of-magnitude change of the muon lifetime under the influence of an electromagnetic field of a CO$_2$ laser, we revisit the issue and show that such claims are nonrealistic.