Generalized Equations and Their Solutions in the (S, 0) ? (0, S) Representations of the Lorentz Group

Quantum Fest 2016 International Conference on Quantum Phenomena, Quantum Control and Quantum Optics

Dvoeglazov, V.V.^1

UAF, Universidad Autónoma de Zacatecas, Apartado Postal 636, Zacatecas, Zac., México

98061, Mexico^1

关键词: Algebraic equations;    Arbitrary spin;    Commutativity;    Dirac equations;    Energy solutions;    Generalized Equations;    Lorentz group;    Relativistic quantum mechanics;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/839/1/012020/pdf
DOI  :  10.1088/1742-6596/839/1/012020

来源: IOP

【 摘 要 】

We present three 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 equation and for u- and v- 4-spinors have solutions with . The same is true for higher-spin equations. Meanwhile, every book considers the equality p0= Epfor both u- and v- spinors of the (1/2, 0) ⊕ (0, 1/2)) representation only, 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. Some applications are discussed.