Looking for new solutions to the hierarchy problem
  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). 
Francesco Caravaglios