  This thesis studies the symmetries and phenomenologies of the massive vector
fields of indefinite spin with both scalar and spin-one degrees of freedom and
Elko. The investigation is conducted by using and extending the quantum field
theory formalism developed by Wigner and Weinberg. In particular, we explore
the possibility that the W^{\pm} and Z bosons have an additional scalar degree
of freedom and show that Elko is a fermionic dark matter candidate. We show
that the massive vector fields of indefinite spin are consistent with Poincare
symmetry and have physically desirable properties that are absent for their
pure spin-one counterpart. Using the new vector fields, the decay of the
W^{\pm} and Z bosons to leptons at tree-level are in agreement with the
Standard Model (SM) predictions. For higher order scattering amplitudes, the
theory has better convergent behaviour than the intermediate vector boson model
and the Fermi theory. Elko has the unusual property that it satisfies the
Klein-Gordon but not the Dirac equation and has mass dimension one instead of
three-half. We show that the Elko fields are local only along a preferred axis
and that they violate Lorentz symmetry. Motivated by the results obtained by
Ahluwalia and Horvath that the Elko spin-sums are covariant under very special
relativity (VSR) transformations, we derive the VSR particle states and quantum
fields. We show that the VSR particles can only interact with the SM particles
through gravity and massive scalar particles thus making them and hence Elko
dark matter candidates.
