Heisenberg model in pseudo-Euclidean spaces II

TL;DR

This paper explores the geometric relationship between the Heisenberg spin chain model on pseudospheres, light-like cones in pseudo-Euclidean spaces, and virtual billiards, providing a new interpretation of integrals similar to Moser's work.

Contribution

It offers a novel geometric interpretation of the integrals of the Heisenberg model in pseudo-Euclidean spaces, extending Moser's approach to new settings.

Findings

Established a relation between Heisenberg model and pseudo-Euclidean geometries

Provided a geometric interpretation of integrals for the model

Connected the model to virtual billiards and confocal quadrics

Abstract

In the review we describe a relation between the Heisenberg spin chain model on pseudospheres and light--like cones in pseudo--Eucli\-dean spaces and virtual billiards. A geometrical interpretation of the integrals associated to a family of confocal quadrics is given, analogous to Moser's geometrical interpretation of the integrals of the Neumann system on the sphere.