  We give a microscopic derivation of the chiral Luttinger liquid theory for
the Laughlin states. Starting from the wave function describing an arbitrary
incompressibly deformed Laughlin state (IDLS) we quantize these deformations.
In this way we obtain the low-energy projections of local microscopic operators
and derive the quantum field theory of edge excitations directly from quantum
mechanics of electrons. This shows that to describe experimental and numeric
deviations from chiral Luttinger liquid theory one needs to go beyond
Laughlin's approximation. We show that in the large N limit the IDLS is
described by the dispersionless Toda hierarchy.
