The Barut Second-Order Equation: Lagrangian, Dynamical Invariants and Interactions

TL;DR

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

Contribution

The authors derive Barut's equation from fundamental principles and investigate its dynamical invariants and interaction effects, providing new insights into lepton mass differences.

Findings

Derived the second-order equation from first principles.

Identified dynamical invariants for the model.

Analyzed the impact 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 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 dynamical invariants for this model, investigating the influence of potential interactions.