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We present a powerful method for exploring various processes in the presenceof strong external fields and matter. The method implies utilization of theexact solutions of the modified Dirac equations which contain the effectivepotentials accounting for the influences of external electromagnetic fields andmatter on particles. We briefly discuss the basics of the method and itsapplications to studies of different processes, including a recently proposednew mechanism of radiation by neutrinos and electrons moving in matter (thespin light of the neutrino and electron). In view of a recent "prediction" ofan order-of-magnitude change of the muon lifetime under the influence of anelectromagnetic field of a CO$_2$ laser, we revisit the issue and show thatsuch claims are nonrealistic.

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