Nonstandard Dirac equations for nonstandard spinors

Generalized Dirac equation with operator mass term is presented. Its solutions are nonstandard spinors (NSS) which, like eigenspinoren des Ladungskonjugationsoperators (ELKO), are eigenvectors of the charge conjugation and dual-helicity operators. It is demonstrated that in spite of their noncovariant nature the NSS can serve as a carrier space of a representation of Poincaré group. However, the corresponding boost generators are not manifestly covariant and generate nonlocal momentum dependent transformations, which are presented explicitly. These results can present a new look on group-theoretical grounds of ELKO theories.

Higher derivative fermionic field equation in the first-orderformalism

The generalized Dirac equation of the third order, describing particles with spin 1/2 and three mass states, is analyzed. We obtain the first-order generalized Dirac equation in the 24-dimensional matrix form. The mass and spin projection operators are found that extract solutions of the wave equation corresponding to pure spin states of particles. The density of the electromagnetic current is obtained, and minimal and nonminimal(anomalous) electromagnetic interactions of fermions are considered by introducing three phenomenological parameters. The Hamiltonian form of the first-order equation is obtained.PACS Nos.: 03.65.Pm, 11.10.Ef; 12.10.Kt