Negative Energies in the Dirac equation

TL;DR

This paper explores the existence of negative energy solutions in the Dirac equation and higher-spin equations, questioning traditional assumptions and examining the implications of Fock space doubling at the quantum field level.

Contribution

It re-examines negative energy solutions in Dirac and higher-spin equations and discusses the possibility of Fock space doubling beyond traditional approaches.

Findings

Negative energy solutions exist for Dirac and higher-spin equations.

Fock space doubling can be considered at the quantum field level.

Traditional treatments may overlook these negative energy states.

Abstract

It is easy to check that both algebraic equation Det (hat p - m) =0 and Det (hat p + m) =0 for u- and v- 4-spinors have solutions with p_0= pm E_p = pm sqrt bf p^2 +m^2. The same is true for higher-spin equations. Meanwhile, every book considers the equality p_0=E_p for both u- and v- spinors of the (1/2,0)+(0,1/2)) representation only, thus applying the Dirac-Feynman-Stueckelberg procedure for elimination of the negative-energy solutions. The recent Ziino works (and, independently, the articles of several others) show that the Fock space can be doubled. We re-consider this possibility on the quantum field level for both s=1/2 and higher spin particles.