Baxter equations and Deformation of Abelian Differentials

TL;DR

This paper proves key properties of deformed Abelian differentials linked to quantum integrable systems, using Baxter equations, and explores their classical limit and duality properties.

Contribution

It provides rigorous proofs of properties of deformed Abelian differentials derived from Baxter equations, including the Riemann bilinear relation, advancing understanding in quantum integrable systems.

Findings

Proof of Riemann bilinear relation for deformed Abelian differentials

Analysis of classical limit of the deformed differentials

Role of duality in the properties of these differentials

Abstract

In this paper the proofs are given of important properties of deformed Abelian differentials introduced earlier in connection with quantum integrable systems. The starting point of the construction is Baxter equation. In particular, we prove Riemann bilinear relation. Duality plays important role in our consideration. Classical limit is considered in details.