TY - JOUR
AU - Cázares, J. A.
AU - Dvoeglazov, Valeriy
PY - 2023/09/01
Y2 - 2024/08/07
TI - Generalized equations and their solutions in the (1/2,0)+(0,1/2) representations of the Lorentz group
JF - Revista Mexicana de Física
JA - Rev. Mex. Fís.
VL - 69
IS - 5 Sep-Oct
SE - 07 Gravitation, Mathematical Physics and Field Theory
DO - 10.31349/RevMexFis.69.050703
UR - https://rmf.smf.mx/ojs/index.php/rmf/article/view/6350
SP - 050703 1–9
AB - <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>
ER -