Mass dimension one fields with Wigner degeneracy: A theory of dark matter

Whatever dark matter is, it must be one irreducible unitary representation of the inhomogeneous Lorentz group or another. We here develop a formalism of mass dimension one fermions and bosons of spin one half, and show that they provide natural dark matter candidates. By construction, they are covariant under space-time translations and boosts. However, incorporating the rotational symmetry is non-trivial and requires introducing a two-fold Wigner degeneracy thus doubling the degrees of freedom for particles and anti particles from two to four. With Wigner degeneracy, we have a well-defined theory of mass dimension one fields of spin one half that are physically distinct from the Dirac field. They are local, Lorentz covariant and have positive definite Hamiltonians. The framework also has the potential to resolve the cosmological constant problem, and supply dark energy.