High Quality Content by WIKIPEDIA articles! The Lichnerowicz formula (also known as the Lichnerowicz–Weitzenbock formula) is a fundamental equation in the analysis of spinors on pseudo-Riemannian manifolds. In dimension 4, it forms a piece of Seiberg–Witten theory and other aspects of gauge theory. It is named after noted mathematician Andre Lichnerowicz who proved it in 1963. The formula gives a relationship between the Dirac operator and the Laplace-Beltrami operator acting on spinors, in which the scalar curvature appears in a natural way. The result is significant because it provides an interface between results from the study of elliptic partial differential equations, results concerning the scalar curvature, and results on spinors and spin structures.

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