Problems with using separated variables for computing expectation values for higher ranks

Abstract

We consider the simplest classical integrable model corresponding to a non-hyperelliptic spectral curve. We show that a certain complicated integral occurs when computing the average of observables in this model. This integral does not factorise. Since similar problems should also exist in the quantum case, we think that a serious question arises of how to deal with these integrals.

15 pages, acknowledgement added