Generalized equations and their solutions in the (1/2,0)+(0,1/2) representations of the Lorentz group


  • J. A. Cázares Ventspils University of Appliend Sciences
  • Valeriy Dvoeglazov Universidad de Zacatecas



Relativistic quantum mechanics; spin-1/2; Dirac-Feynman-Stueckelberg


We present explicit examples of generalizations in relativistic quantum mechanics. First of all, we 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 equations Det(ˆp − m) = 0 and Det(ˆp + m) = 0 for u− and v− 4-spinors have solutions with p0 = ±Ep = ± p 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, thus applying the DiracFeynman-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 re-consider this possibility on the quantum field level for both S = 1/2 and higher spin particles. The third example is: we postulate the non-commutativity of 4-momenta, and we derive the mass splitting in the Dirac equation. The applications are discussed.

Author Biography

Valeriy Dvoeglazov, Universidad de Zacatecas

UAF, Profesor Titular C


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How to Cite

J. A. Cázares and V. Dvoeglazov, “Generalized equations and their solutions in the (1/2,0)+(0,1/2) representations of the Lorentz group”, Rev. Mex. Fís., vol. 69, no. 5 Sep-Oct, pp. 050703 1–, Sep. 2023.



07 Gravitation, Mathematical Physics and Field Theory