2012/11/30 by Maxim Dvornikov, D. M. Gitman, Д. М. Гитман
Physics and Astronomy · #Dark Matter and Cosmic Phenomena #Neutrino Physics Research #Particle physics theoretical and experimental studies #hep-ph #hep-th
paper · pdf · doi:10.1103/physrevd.87.025027
published as Physical Review D 87, 025027 (2013) · 9 pages, two columns, no figures, Revtex 4.1; paper was significantly revised, the new Sec. III was added, Sec. VI was extended, 9 new references were included, version to be published in Phys.Rev.D
arxiv created 2013/01/19 · openalex publication_date 2013/01/24 · arxiv updated 2013/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
We study massive 1/2-spin particles in various external backgrounds, keeping in mind applications to neutrino physics. We are mainly interested in massive Majorana (Weyl) fields. However, massive neutral Dirac particles are also considered. We formulate classical Lagrangian theory of the massive Weyl field in terms of Grassmann-odd two-component spinors. Then, we construct the Hamiltonian formulation of such a theory, which turns out to be a theory with second-class constraints. Using this formulation, we canonically quantize the massive free Weyl field. We derive propagators of the Weyl field and relate them to the propagator of a massive Dirac particle. We also study the massive Weyl particles propagating in the background mater. We find the path integral representation for the propagator of such a field, as well as the corresponding pseudoclassical particle action. The massless limit of the Weyl field interacting with the matter is considered and compared with results of other works. Finally, the path integral representation for the propagator of the neutral massive Dirac particle with an anomalous magnetic moment moving in the background matter and external electromagnetic field, as well as the corresponding pseudoclassical particle action, are constructed.