Explicit expressions for the expectation values and the variances of some
observables, which are bilinear quantities in the quantum fields on a
D-dimensional manifold, are derived making use of zeta function regularization.
It is found that the variance, related to the second functional variation of
the effective action, requires a further regularization and that the relative
regularized variance turns out to be 2/N, where N is the number of the fields,
thus being independent on the dimension D. Some illustrating examples are
worked through.Comment: 15 pages, latex, typographical mistakes correcte