  In ordinary Quantum Mechanics only ideally instantaneous observations of a
quantity or a set of compatible quantities are usually considered. In an old
paper of our group in Milano a formalism was introduced for the continuous
monitoring of a system during a certain interval of time in the framework of a
somewhat generalized approach to Q. M. The outcome was a distribution of
probability on the space of all the possible continuous histories of a set of
quantities to be considered as a kind of coarse grained approximation to some
ordinary quantum observables commuting or not. The main aim was the
introduction of a classical level in the context of Quantum Mechanics, treating
formally a set of basic quantities {\it to be considered as beables} in the
sense of Bell as continuously taken under observation. However the effect of
such assumption was a permanent modification of the Liouville-von Neumann
equation for the statistical operator by the introduction of a dissipative term
which is in conflict with basic conservation rules in all reasonable models we
had considered. Difficulties were even encountered for a relativistic extension
of the formalism. In this paper I propose a modified version of the original
formalism which seems to overcome both difficulties. First I study the simple
models of an harmonic oscillator and a free scalar field in which a coarse
grain position and a coarse grained field respectively are treated as beables.
Then I consider the more realistic case of Spinor Electrodynamics in which only
certain coarse grained electric and magnetic fields and no matter related
quantities are introduced as classical variables.
