  The objective of this paper is to clarify the relationships between the
quantum D-module and equivariant Floer theory. Equivariant Floer theory was
introduced by Givental in his paper ``Homological Geometry''. He conjectured
that the quantum D-module of a symplectic manifold is isomorphic to the
equivariant Floer cohomology for the universal cover of the free loop space.
First, motivated by the work of Guest, we formulate the notion of ``abstract
quantum D-module''which generalizes the D-module defined by the small quantum
cohomology algebra. Second, we define the equivariant Floer cohomology of toric
complete intersections rigorously as a D-module, using Givental's model. This
is shown to satisfy the axioms of abstract quantum D-module. By Givental's
mirror theorem, it follows that equivariant Floer cohomology defined here is
isomorphic to the quantum cohomology D-module.
