Infinite Dimensional Symmetries of Self-Dual Yang-Mills

TL;DR

This paper constructs an infinite-dimensional Lie algebra of symmetries for self-dual Yang-Mills theory using a canonical transformation, revealing deep algebraic structures in the theory.

Contribution

It introduces a novel method to derive symmetries of self-dual Yang-Mills via a canonical transformation to a free theory, uncovering an infinite-dimensional algebra.

Findings

Symmetries form an infinite-dimensional Lie algebra.

The algebra is constructed in the group algebra of isometries.

The approach links symmetries to canonical transformations.

Abstract

We construct symmetries of the Chalmers-Siegel action describing self-dual Yang-Mills theory using a canonical transformation to a free theory. The symmetries form an infinite dimensional Lie algebra in the group algebra of isometries.