On the Hamiltonian Form of Generalized Dirac Equation for Fermions with Two Mass States

We continue to investigate the first order generalized Dirac equation (FOGDE), describing fermions with spin 1/2 and two mass states. This 20-component wave equation was obtained in [1] on the base of Barut’s [2] second order equation describing particles with two mass states. Barut suggested the second order wave equation for the unified description of e, μ leptons. He treated this equation as an effective equation for partly “dressed” fermions using the non-perturbative approach to quantum electrodynamics. Some investigations of Barut’s second order wave equation and FOGDE were performed in [3], [4], [5], [6], [7]. The purpose of this paper is to obtain the Hamiltonian Form of the 20component wave equation of the first order. The paper is organized as follows. In Sec. 2, we introduce the generalized Dirac equation of the first order. The dynamical and non-dynamical components of the 20-component wave function are separated, and quantummechanical Hamiltonian is derived in Sec. 3. In Sec. 4, we make a conclusion. In Appendix, we give some useful matrices entering the Hamiltonian. The system of units h̄ = c = 1 is chosen, Latin letters run 1, 2, 3, and Greek letters run 1, 2, 3, 4, and notations as in [8] are used.