Valeriy V. Dvoeglazov
On Negative-Energy 4-Spinors and Masses in the Dirac Equation
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ABSTRACT.  Both algebraic equation $Det (\hat p - m) =0$ and $Det (\hat p + m) =0$ for $u-$ and $v-$ 4-spinors have solutions with $p_0= \pm E_p =\pm \sqrt{{f p}^2 +m^2}$. The same is true for higher-spin equations (or they may even have more complicated dispersion relations). Meanwhile, every book considers the equality $p_0=E_p$ for both $u-$ and $v-$ spinors of the $(1/2,0)\oplus (0,1/2))$ 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 for both $s=1/2$ and higher spin particles.