  We present a microscopic derivation of the hydrodynamic theory of the Quantum
Hall smectic or stripe phase of a two-dimensional electron gas in a large
magnetic field. The effective action of the low energy is derived here from a
microscopic picture by integrating out high energy excitations with a scale of
the order the cyclotron energy.The remaining low-energy theory can be expressed
in terms of two canonically conjugate sets of degrees of freedom: the
displacement field, that describes the fluctuations of the shapes of the
stripes, and the local charge fluctuations on each stripe.
