English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

In this talk I present three explicit examples of generalizations inrelativistic quantum mechanics.  First of all, I discuss the generalized spin-1/2 equations for neutrinos.They have been obtained by means of the Gersten-Sakurai method for derivationsof arbitrary-spin relativistic equations. Possible physical consequences arediscussed. Next, it is easy to check that both Dirac algebraic equation $Det(\hat p - m) =0$ and $Det (\hat p + m) =0$ for $u-$ and $v-$ 4-spinors havesolutions with $p_0= \pm E_p =\pm \sqrt{{\bf p}^2 +m^2}$. The same is true forhigher-spin equations. Meanwhile, every book considers the equality $p_0=E_p$for both $u-$ and $v-$ spinors of the $(1/2,0)\oplus (0,1/2))$ representationonly, thus applying the Dirac-Feynman-Stueckelberg procedure for elimination ofthe negative-energy solutions. The recent Ziino works (and, independently, thearticles of several others) show that the Fock space can be doubled. Were-consider this possibility on the quantum field level for both $S=1/2$ andhigher spin particles. The third example is: we postulate the non-commutativityof 4-momenta, and we derive the mass splitting in the Dirac equation. Theapplications are discussed.Comment: 20 pp., Talk at the 31st International Colloquium on Group  Theoretical Methods in Physics, Rio de Janeiro, Brasil, JUne 19-25, 201

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