http://arxiv.org/abs/1810.04985
Under rotations by an angle $\vartheta$, both the right- and left- handed Weyl spinors pick up a phase factor ${\exp(\pm\, i \vartheta/2)}$. The upper sign holds for the positive helicity spinors, while the lower sign for the negative helicity spinors. For $\vartheta = 2\pi$ 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 $2\pi$ 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 (Weinberg 2005, Ahluwalia 2017). And the rotation induced phases, being same, factor out. But for the eigenspinors of the charge conjugation operator 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 is more subtle: for $0<\vartheta<2\pi$ a self conjugate spinor becomes a linear combination of the self-antiself conjugate spinors times a $\vartheta$ dependent phase factor. This new effect, to the best of our knowledge, has never been reported before. The purpose of this communication is to present the unexpected result and its possible consequences for a dark matter candidate described by the mass dimension one fermions.
D. Ahluwalia and S. Sarmah
Fri, 12 Oct 18
44/59
Comments: 7 pages