Zamolodchikov Tetrahedral Equation and Higher Hamiltonians of 2d Quantum Integrable Systems

TL;DR

This paper introduces a new method for constructing higher Hamiltonians in 2D quantum integrable systems linked to the Zamolodchikov tetrahedral equation, extending previous approaches to generic solutions without spectral parameters.

Contribution

It presents an effective construction method for higher Hamiltonians associated with the tetrahedral equation, generalizing existing techniques to broader solutions.

Findings

Constructs higher Hamiltonians for generic tetrahedral solutions

Extends the method to solutions without spectral parameters

Links the tetrahedral equation to 2-knot quasi-invariants

Abstract

The main aim of this work is to develop a method of constructing higher Hamiltonians of quantum integrable systems associated with the solution of the Zamolodchikov tetrahedral equation. As opposed to the result of V.V. Bazhanov and S.M. Sergeev the approach presented here is effective for generic solutions of the tetrahedral equation without spectral parameter. In a sense, this result is a two-dimensional generalization of the method by J.-M. Maillet. The work is a part of the project relating the tetrahedral equation with the quasi-invariants of 2-knots.