Valeriy V. Dvoeglazov
Solutions in the (1/2, 0) + (0, 1/2) Representation of the 
Lorentz Group
(288K, PDF)

ABSTRACT.  I present explicit examples of generalizations in relativistic quantum mechanics. First of all, I discuss the generalized spin-1/2 equations for neutrinos. They have been obtained 
by means of the Gersten-Sakurai method for derivations of arbitrary-spin relativistic equations. Possible physical consequences are discussed. Next, it is easy to check that both Dirac algebraic 
equation Det( p − m) = 0 and Det( p + m) = 0 for u− and v− 4-spinors have solutions with p0 = Ep = sqrt{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 work by Ziino (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 S = 1/2 particles. The third example is: we postulate the noncommutativity of 4-momenta, and we derive the mass splitting in the Dirac equation. Some applications are discussed.