Under a rotation by an angle ϑ, both the right- and left-handed 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 four-component spinors are built from a direct sum of the indicated two-component 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 left-transforming components have the same helicity. And the rotation-induced phases, being the same, factor out. But for the eigenspinors of the charge conjugation operator, i.e., Elko, the left- and right-transforming 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 self-conjugate spinor becomes a linear combination of the self- and antiself-conjugate spinors with ϑ -dependent superposition coefficients -and yet the rotation preserves the self-/antiself-conjugacy 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.
EPL (Europhysics Letters)
- Pub Date:
- February 2019
- High Energy Physics - Theory;
- Astrophysics - Astrophysics of Galaxies;
- General Relativity and Quantum Cosmology
- 7 pages, Two new sections, and significantly new material. An error in v1 and v2 corrected