Generalized equations and their solutions in the (1/2,0)+(0,1/2) representations of the Lorentz group (9 pages)

• J.A. Cázares ^[2] ; V.V. Dvoeglazov ^[1]
  1. [1] Universidad Autónoma de Zacatecas

     Universidad Autónoma de Zacatecas

     México

     
  2. [2] Ventspils University of Appliend Sciences. Latvia
• Localización: Revista Mexicana de Física, ISSN-e 0035-001X, Vol. 69, Nº. 5, 2023
• Idioma: inglés
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• Resumen

  • 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(p̂ − m) = 0 and Det(p̂ + m) = 0 for u – and v − 4-spinors have solutions with p_(0) = ± Ep = ± √(p^(2)+m^(2)). The same is true for higher-spin equations. Meanwhile, every book considers the equality p_(0) = E_(p) for both u – and v − spinors of the (1/2,0) ⊕ (0,1/2) representation, 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 re-consider this possibility on the quantum field level for both S = ½ 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.