  Whatever dark matter is, it must be one irreducible unitary representation of
the extended 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 free
Hamiltonians. The developed framework also has the potential to resolve the
cosmological constant problem, and supply dark energy.
