Resumo

CAZARES, J. A.  e  DVOEGLAZOV, V. V.. Generalized equations and their solutions in the (1/2,0)+(0,1/2) representations of the Lorentz group. Rev. mex. fis. [online]. 2023, vol.69, n.5.  Epub 28-Out-2024. ISSN 0035-001X.  https://doi.org/10.31349/revmexfis.69.050703.

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 $Det(\widehat{p}-m)=0$ and $Det(\widehat{p}+m)=0$ for u - and v - 4-spinors have solutions with $p_0=\pm E_p=\pm \sqrt{p^2+m^2}$. 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 $(1/\mathrm{2,0})\oplus (\mathrm{0,1}/2)$ 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 = 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.

Palavras-chave : Relativistic quantum mechanics; spin-1/2; Dirac-Feynman-Stueckelberg.

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