Reduction formulae for multipole states

A model of scalar fields doublet is considered and the conditions for the appearance of a dipole state are elucidated. A reduction formula is considered, and the unit operator representation is obtained in the state space by means of the Green functions. The reduction formula was generalized on the case of eta-pole states. As an example reduction formulae are constructed for QED and for the non-physical part of Ωsub(β)sup(e)=(Asub(μ)sup(e), Bsup(e)) field in a spontaneously violated gauge theory. All the relations are shown to have a standard form and to be analogous to those for the phi (x) field