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

Understand

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.