@article{Cázares_Dvoeglazov_2023, title={Generalized equations and their solutions in the (1/2,0)+(0,1/2) representations of the Lorentz group}, volume={69}, url={https://rmf.smf.mx/ojs/index.php/rmf/article/view/6350}, DOI={10.31349/RevMexFis.69.050703}, abstractNote={<p>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.</p>}, number={5 Sep-Oct}, journal={Revista Mexicana de Física}, author={Cázares, J. A. and Dvoeglazov, Valeriy}, year={2023}, month={Sep.}, pages={050703 1–} }