Negative Energies in the Dirac Equation (original) (raw)

It is easy to check that both algebraic equation Det(p − m) = 0 and Det(p + m) = 0 for u− and v− 4-spinors have solutions with p0 = ±Ep = ± p 2 + m 2. The same is true for higher-spin equations. Meanwhile, every book considers the equality p0 = Ep 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 reconsider this possibility on the quantum field level for both s = 1/2 and higher spin particles.