  In this paper we investigate the question how spontaneous symmetry breaking
works in the framework of Loop Quantum Gravity and we compare it to the results
obtained in the case of the Proca field, where we were able to quantise the
theory in Loop Quantum Gravity without introducing a Higgs field. We obtained
that the Hamiltonian of the two systems are very similar, the only difference
is an extra scalar field in the case of spontaneous symmetry breaking. This
field can be identified as the field that carries the mass of the vector field.
In the quantum regime this becomes a well defined operator, which turns out to
be a self adjoint operator with continuous spectrum. To calculate the spectrum
we used a new representation in the case of the scalar fields, which in
addition enabled us to rewrite the constraint equations to a finite system of
linear partial differential equations. This made it possible to solve part of
the constraints explicitly.
