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In mathematics, mixed Hodge modules are the culmination of Hodge theory, mixed Hodge structures, intersection cohomology, and the decomposition theorem yielding a coherent framework for discussing variations of degenerating mixed Hodge structures through the six functor formalismEssentially, these objects are a pair of a filtered Dmodule (,) together with a perverseIH,"(X) x IH~(X) ~ IH,'(X) ~ Z is nondegenerate when tensored with the rationals For a compact oriented manifold, all the intersection homology groups coincide with ordinary homology and cohomology (913) For normal spaces (a class of pseudomanifolds including normal complex algebraic varieties, see 44As N!1the sum becomes an integral over all time and we write K(x N;x 0) = Z Dx(t) Z Dp(t)expi ~ Z T 0 dt(_xp H(x;p)) This is the phase space path integral If the Hamiltonian has the standard form

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