A toy model for relativistic neutrino masses

We propose a toy model to study Dirac charged leptons and their associated antineutrinos in the presence of a homogeneous magnetic field within the framework of relativistic quantum mechanics. The discussion is kept concrete by reducing the space dimensions to 2, considering 'spinless antineutrinos' in 2 + 1 space-time dimensions. Solutions to specific problems in particle physics are often hindered by the technical complexities encountered in $(3+1)$-dimensions. In such cases, it is convenient to have a lower space dimensional model at ones disposal that captures some physical features while reducing technical difficulties to a minimum. The content of this article is suitable for graduate students in theoretical and experimental particle physics. (paper)