Commuting Hamiltonians from Seiberg-Witten Theta-Functions

TL;DR

This paper uses computational methods to support the idea that ratios of theta-functions from Seiberg-Witten curves form Poisson-commuting Hamiltonians, advancing understanding of integrable systems in theoretical physics.

Contribution

It provides computational evidence that theta-function ratios serve as Poisson-commuting Hamiltonians in Seiberg-Witten integrable systems.

Findings

Ratios of theta-functions are Poisson-commuting Hamiltonians.

Computational support for the duality in Seiberg-Witten systems.

Confirmation of theoretical predictions using MAPLE calculations.

Abstract

Elementary MAPLE calculations are used to support the claim of hep-th/9906240 that the ratios of theta-functions, associated with the Seiberg-Witten complex curves, provide Poisson-commuting Hamiltonians which describe the dual of the original Seiberg-Witten integrable system.