Non-standard Dirac equations for non-standard spinors

Abstract: Generalized Dirac equation with operator mass term is presented. Its solutions are non standard (ELKO) spinors which are eigenvectors of the charge conjugation and dual helicity operators. It is demonstrated that in spite of their non covariant nature ELKO can serve as a carrier space of a representation of Poincar\'e group. However, the corresponding boost generators are not manifestly covariant and generate non-local momentum dependent transformations which are presented explicitly. These results present a new look on group-theoretical grounds of ELKO theories.