Electromagnetic properties of non-Dirac particles with rest spin 1/2

TL;DR

This paper develops an analytic framework for describing electromagnetic form factors of non-Dirac spin-1/2 particles, matching experimental proton data without assuming internal structure.

Contribution

It introduces a general antisymmetric tensor operator structure and recurrence relations for Lorentz group transformations, advancing the theoretical understanding of non-Dirac particles.

Findings

Form factors decrease with increasing Q^2, matching experimental proton data.

Explicit formulas for Lorentz transformation matrix elements are derived.

The approach models electromagnetic properties without internal particle assumptions.

Abstract

We resolve a number of questions related to an analytic description of electromagnetic form factors of non-Dirac particles with the rest spin 1/2. We find the general structure of a matrix antisymmetric tensor operator. We obtain two recurrence relations for matrix elements of finite transformations of the proper Lorentz group and explicit formulas for a certain set of such elements. Within the theory of fields with double symmetry, we discuss writing the components of wave vectors of particles in the form of infinite continued fractions. We show that for $Q^{2} \leq 0.5$ (GeV/c)$^{2}$, where $Q^{2}$ is the transferred momentum squared, electromagnetic form factors that decrease as $Q^{2}$ increases and are close to those experimentally observed in the proton can be obtained without explicitly introducing an internal particle structure.