Massive spin-one-half one-particle states for the mass-dimension-one fermions

Abstract

We study the conditions under which a non-standard Wigner class concerning discrete symmetries may arise for massive spin one-half states. The mass dimension one fermionic states are shown to constitute explicit examples. We also show how to conciliate these states with the current criticism due to the Lee and Wick, and Weinberg formulation.

Flag-dipole spinors: On the dual structure derivation and $${\mathcal {C}}$$, $${\mathcal {P}}$$ and $${\mathcal {T}}$$ symmetries

“…We shall finalize making allusive comments about the flag-dipole spinors behaviour under action of (CPT ) 2 . As previously mentioned, the unexpected outcome obtained in Sect.3 was predicted by Wigner, and later revisited in [26]. Hence, this is the second case reported in the current literature of an entity that fits Wigner's non-standard classes, being a fermion with unexpected features, carrying similar features to the Elko spinors.…”

“…Thus, both Elko and flag-dipole spinors show congruous features. Such result combined with the above calculations evince that flag-dipole spinors also belong to the Wigner Class 3 [2] and may also belong to the degenerated Hilbert space [26]. Note that for the second time this behaviour is reported for a fermion.…”

Spin-1/2 "bosons'' with mass dimension 3/2 and fermions with mass dimension 1 cannot represent physical particle states

“…where σ k , k = 1, 2, 3 are the Pauli matrices. Substituting the above matrix representations in conditions (10) and ( 11), we obtain…”

“…By considering (u ± (0, s)) i and (v ± (0, s)) i as the (i, s) elements of corresponding matrices U ± and V ± , we can rewrite conditions (10) and (11) in matrix form…”

“…Weinberg argued, after a revision of the Wigner's results that the non-usual fermionic classes found by Wigner do not exist in quantum field theory [8]. However, the current literature may provide some clear examples of particles populating such classes [9,10].…”