2016/07/05 by Dvoeglazov, Valeriy V.
#FOS: Physical sciences #General Physics (physics.gen-ph) #High Energy Physics - Theory (hep-th)
paper · doi:10.48550/arxiv.1607.03011
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 =± √\bf p2 +m2. 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 non-commutativity of 4-momenta, and we derive the mass splitting in the Dirac equation. Some applications are discussed.