  While in first and second quantization the fundamental operators are
respectively coordinates and fields (functions), an extension of quantum field
theory can be achieved if the usual pair of conjugate momenta is represented by
functionals. After a brief introduction on the hierarchy problem, we show how
the ordinary quantum field theory can arise from a specific limit of this
extension. We will also show how this extension can offer new solutions to the
hierarchy problem. The peculiarity that makes this scenario appealing (as
possible solution of the hierarchy problem), is the absence of new light
particles at (or close to) the electroweak scale. This is in much better
agreement with the experimental observation, since (until now) all searches for
new physics signals have confirmed the remarkable success of the Standard Model
(contrary to common expectations).
