On negative energy 4-spinors and masses in the Dirac equation

Abstract

Both algebraic equations [Formula: see text] and [Formula: see text] for [Formula: see text]- and [Formula: see text]- 4-spinors have solutions with [Formula: see text]. The same is true for higher-spin equations (or they may even have more complicated dispersion relations). Meanwhile, every book considers the equality [Formula: see text] for both [Formula: see text]- and [Formula: see text]-spinors of the [Formula: see text] representation only, thus applying the Dirac–Feynman–Stueckelberg procedure for elimination of negative-energy solutions. The recent Ziino works (and, independently, the articles of several other authors) show that the Fock space can be doubled. We re-consider this possibility on the quantum-field level.