  The classical notions of continuity and mechanical causality are left in
order to refor- mulate the Quantum Theory starting from two principles: I) the
intrinsic randomness of quantum process at microphysical level, II) the
projective representations of sym- metries of the system. The second principle
determines the geometry and then a new logic for describing the history of
events (Feynman's paths) that modifies the rules of classical probabilistic
calculus. The notion of classical trajectory is replaced by a history of
spontaneous, random an discontinuous events. So the theory is reduced to
determin- ing the probability distribution for such histories according with
the symmetries of the system. The representation of the logic in terms of
amplitudes leads to Feynman rules and, alternatively, its representation in
terms of projectors results in the Schwinger trace formula.
