[en] It is shown, that the effective action of Berry phase type is connected with some one-dimensional models with long-range 1/r²-interaction. In particular, the Caldeira-Leggett action for Josephson junction with dissipation and classical spin systems are related with local effective action of holomorphic Berry phase type through the Hilbert reduction. Some consequences of this relation are discussed, including conformal symmetry of Caldeira-Leggett action and a possibility of exact solution of these models. (author). 19 refs