Elko under spatial rotations
Abstract
Under a rotation by an angle ϑ, both the right and lefthanded Weyl spinors pick up a phase factor \exp(+/ i \vartheta/2) . The upper sign holds for the positive helicity spinors, while the lower sign holds for the negative helicity spinors. For \vartheta = 2π radians this produces the famous minus sign. However, the fourcomponent spinors are built from a direct sum of the indicated twocomponent spinors. The effect of the rotation by 2π radians on the eigenspinors of the parity  that is, the Dirac spinors  is the same as on Weyl spinors. It is because for these spinors the right and lefttransforming components have the same helicity. And the rotationinduced phases, being the same, factor out. But for the eigenspinors of the charge conjugation operator, i.e., Elko, the left and righttransforming components have opposite helicities, and, therefore, they pick up opposite phases. As a consequence the behaviour of the eigenspinors of the charge conjugation operator (Elko) is more subtle: for 0<\vartheta<2π a selfconjugate spinor becomes a linear combination of the self and antiselfconjugate spinors with ϑ dependent superposition coefficients and yet the rotation preserves the self/antiselfconjugacy of these spinors! This apparently paradoxical situation is fully resolved. This new effect, to the best of our knowledge, has never been reported before. The purpose of this communication is to present this result and to correct an interpretational error of a previous version.
 Publication:

EPL (Europhysics Letters)
 Pub Date:
 February 2019
 DOI:
 10.1209/02955075/125/30005
 arXiv:
 arXiv:1810.04985
 Bibcode:
 2019EL....12530005V
 Keywords:

 High Energy Physics  Theory;
 Astrophysics  Astrophysics of Galaxies;
 General Relativity and Quantum Cosmology
 EPrint:
 7 pages, Two new sections, and significantly new material. An error in v1 and v2 corrected