The Barut Second-Order Equation, Dynamical Invariants and Interactions

Abstract

The second-order equation in the (1/2,0)+(0,1/2) representation of the Lorentz group has been proposed by A. Barut in the beginning of the 70s. It permits to explain the mass splitting of leptons e,mu,tau. Recently, the interest has grown to this model (see, for instance, the papers by S. Kruglov and J. P. Vigier et al.). We continue the research deriving the equation from the first principles, finding the dynamical invariants for this model, investigating the influence of the potential interactions.