  In modern physics, one of the greatest divides is that between space-time and
quantum fields, as the fiber bundle of the Standard Model indicates. However on
the operational grounds the fields and spacetime are not very different. To
describe a field in an experimental region we have to assign coordinates to the
points of that region in order to speak of the "when" and "where" of the field
itself. But to operationally study the topology and to coordinatize the region
of spacetime, the use of radars (to send and receive electromagnetic signals)
is required. Thus the description of fields (or, rather, processes) and the
description of space-time are indistinguishable at the fundamental level.
Moreover, classical general relativity already says -- albeit preserving the
fiber bundle structure -- that spacetime and matter are intimately related. All
this indicates that a new theory of elementary processes (out of which all the
usual processes of creation, annihilation and propagation, and consequently the
topology of spacetime itself would be constructed) has to be devised.
  In this thesis I present the foundations of such a finite, discrete,
algebraic, quantum theory and apply it to the description of spin-1/2 quanta of
the Standard Model.
