Generalizations of the Dirac equation in covariant and Hamiltonian form

Abstract

The Dirac wave equation can be treated equally in covariant and Hamiltonian forms. Recently the equations in Hamiltonian form which are in some sense the generalizations of the Dirac Hamiltonian form to the arbitrary spin case have become popular. Here we give similar generalization in the covariant form for the field with n bispinor indices and investigate the physics behind these two generalizations. We show that both generalizations are related to the representations of the de Sitter group and give the multiplets with certain mass and spin. It appears that covariant and Hamiltonian forms are not physically equivalent, the latter one offers nonphysical solutions which should be eliminated using some sort of additional conditions.