The Barut Second-Order Equation, Dynamical Invariants and Interactions

TL;DR

This paper revisits Barut's second-order equation for leptons, deriving it from first principles, analyzing its dynamical invariants, and exploring the effects of potential interactions to better understand lepton mass splitting.

Contribution

It derives Barut's equation from fundamental principles, identifies its dynamical invariants, and examines the impact of interactions, advancing theoretical understanding of lepton mass differences.

Findings

Derived the second-order equation from first principles.

Identified dynamical invariants for the model.

Analyzed the influence of potential 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.