 1929 Valeriy V. Dvoeglazov
 Solutions in the (1/2, 0) + (0, 1/2) Representation of the
Lorentz Group
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Apr 3, 19

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Abstract. I present explicit examples of generalizations in relativistic quantum mechanics. First of all, I discuss the generalized spin1/2 equations for neutrinos. They have been obtained
by means of the GerstenSakurai method for derivations of arbitraryspin 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− 4spinors have solutions with p0 = Ep = sqrt{p^2 + m^2}. The same is true for higherspin 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 DiracFeynmanStueckelberg procedure for elimination of the negativeenergy solutions. The recent work by Ziino (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 S = 1/2 particles. The third example is: we postulate the noncommutativity of 4momenta, and we derive the mass splitting in the Dirac equation. Some applications are discussed.
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