TITLE: Application of Hodge decomposition
QUESTION [7 upvotes]: Hodge decomposition states any $p$ form can be decomposed into three orthogonal $L^2$ components: exact form, co-exact form and hamonic form. But actually we don't know how to decompose a general one. So how to apply the decomposition to other fields? Even if we can decompose one, what does it imply?

REPLY [2 votes]: For the interplay of Hodge theory and physics, see various papers of Cantarella, deTurck, and Gluck.