  In resonance to a recent geometric framework proposed by Douglas and Yang, a
functional model for certain linear bounded operators with rank-one
self-commutator acting on a Hilbert space is developed. By taking advantage of
the refined existing theory of the principal function of a hyponormal operator
we transfer the whole action outside the spectrum, on the resolvent of the
underlying operator, localized at a distinguished vector. The whole
construction turns out to rely on an elementary algebra body involving analytic
multipliers and Cauchy transforms. A natural field theory interpretation of the
resulting resolvent functional model is proposed.
