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

A field theoretic operator model and Cowen-Douglas class