The Symmetry Structure of the Heavenly Equation

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• 作者：Eleonora Alfinito ; Giulio Soliani and Luigi Solombrino
• 关键词：heavenly equation ; symmetry reduction ; infinite ; dimensional Lie algebras ; gravitational instantons and merons.
• 刊名：Letters in Mathematical Physics
• 出版年：1997
• 出版时间：1997
• 年：1997
• 卷：41
• 期：4
• 页码：379-389
• 全文大小：127 KB

文摘

We show that excitations of physical interest for the heavenly equation are generated by symmetry operators which yield two reduced equations with different characteristics. One equation is of the Liouville type and gives rise to gravitational instantons, including those found by Eguchi–Hanson and Gibbons–Hawking. The second equation appears for the first time in the theory of heavenly spaces and provides meron-like configurations endowed with a fractional topological charge. A link is also established between the heavenly equation and the so-called Schröder equation, which plays a crucial role in the bootstrap model and in renormalization theory.