  Starting from a differential equation for the unique field, the equation for
the generating vector |V> of the n-point information (correlation and smeared
functions) in the free Fock space is derived. In derived equation, due to
appropriate extension of the right invertible operators, the physical vacuum
vector |0> appears with a global characteristic of the field. For so called
resolvent regularization of the original systems, the closed equations for the
n-point information are analysed with the help of functional calculus.
