  The quantization rules recently proposed by M. Navarro (and independently
I.V. Kanatchikov) for a finite-dimensional formulation of quantum field theory
are applied to the Klein-Gordon and the Dirac fields to obtain the quantum
equations of motion of both fields. In doing so several problems arise.
  Solving these difficulties leads us to propose a new classical canonical
formalism, which, in turn, leads us to new, improved rules of quantization. We
show that the new classical equations of motion and rules of quantization
overcome several known unsatisfactory features of the previous formalism. We
argue that the new formalism is a general improvement with respect to the
previous one.
  Further we show that the quantum field theory of the Dirac and Klein-Gordon
field describes particles with extra, harmonic-oscillator-like degrees of
freedom. We argue that these degrees of freedom should give rise to a
multi-particle interpretation of the formalism.
