Article,
Generalized Equations and Their Solutions in the (S,0)+(0,S) Representations of the Lorentz Group
(2016)cite arxiv:1607.03011Comment: 20 pp., Talk at the 31st International Colloquium on Group Theoretical Methods in Physics, Rio de Janeiro, Brasil, JUne 19-25, 2016.
Abstract
In this talk I present three explicit examples of generalizations in
relativistic 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 derivations
of arbitrary-spin relativistic equations. Possible physical consequences are
discussed. Next, it is easy to check that both Dirac algebraic equation $Det
(p - m) =0$ and $Det (p + m) =0$ for $u-$ and $v-$ 4-spinors have
solutions with $p_0= E_p =p^2 +m^2$. 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 $(1/2,0)(0,1/2))$ 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. The
applications are discussed.
