Nonmass Eigenstates of Fermion and Boson Fields

TL;DR

This paper explores the concept of nonmass eigenstates in relativistic fields by extending to a five-dimensional framework, deriving equations for various spins, and analyzing the properties of gauge fields coupled to these states.

Contribution

It introduces a novel five-dimensional approach to describe nonmass eigenstates and derives the corresponding field equations, including mass calculations and gauge field analysis.

Findings

Klein-Gordon, Dirac, and Proca equations describe mass eigenstates only.

Rest mass of spin 1/2 field and squared mass of bosons are calculated.

Gauge bosons can be massive when coupled to nonmass eigenstates.

Abstract

It appears natural to consider the four dimensional relativistic massive field as a five dimensional massless field. If the fifth coordinate is interpreted as the proper time, then the fifth moment can be understood as the rest mass. After introducing the rest mass operator, we define the mass eigenstate and the nonmass eigenstate. The general equations of spin 0, spin 1/2 and spin 1 fields are obtained respectively. It is shown that the Klein-Gordon equation, the Dirac equation and the Proca equation describe the mass eigenstates only. The rest mass of spin 1/2 field and the rest mass squared of Boson fields are calculated. The U(1) gauge field that couples to the nonmass eigenstates is studied carefully, whose gauge boson can be massive.