On the spectra of atoms and hadrons

TL;DR

This paper introduces a new non-Hermitian operator for relativistic closed systems that accurately captures the spectra of atoms and hadrons, ensuring proper relativistic kinematics in decay processes.

Contribution

It proposes a novel operator with fewer components than Dirac's, generalizes it to a Klein-Gordon framework, and addresses relativistic kinematics in radiative decays.

Findings

Operator's eigenvalues match squared total energy in CMS

Wave function has half as many components as Dirac's

Ensures relativistic kinematics in radiative decay processes

Abstract

For relativistic closed systems, an operator is explained which has as stationary eigenvalues the squares of the total cms energies, while the wave function has only half as many components as the corresponding Dirac wave function. The operator's time dependence is generalized to a Klein-Gordon equation. It ensures relativistic kinematics in radiative decays. The new operator is not hermitian.