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We study massive 1/2-spin particles in various external backgrounds keepingin mind applications to neutrino physics. We are mainly interested in massiveMajorana (Weyl) fields. However, massive neutral Dirac particles are alsoconsidered. We formulate classical Lagrangian theory of the massive Weyl fieldin terms of Grassmann-odd two-component spinors. Then we construct theHamiltonian formulation of such a theory, which turns out to be a theory withsecond-class constraints. Using this formulation we canonically quantize themassive free Weyl field. We derive propagators of the Weyl field and relatethem to the propagator of a massive Dirac particle. We also study the massiveWeyl particles propagating in the background mater. We find the path integralrepresentation for the propagator of such a field, as well as the correspondingpseudoclassical particle action. The massless limit of the Weyl fieldinteracting with the matter is considered and compared with results of otherworks. Finally, the path integral representation for the propagator of theneutral massive Dirac particle with an anomalous magnetic moment moving in thebackground matter and external electromagnetic field, as well as thecorresponding pseudoclassical particle action are constructed.

Canonical quantization, path integral representations, and pseudoclassical description of massive Weyl neutrinos in external backgrounds