  Using the orbital-free density functional theory as a model theory, we
present an analysis of the field theoretic approach to quasi-continuum method.
In particular, by perturbation method and multiple scale analysis, we provide a
formal justification for the validity of the coarse-graining of various fields,
which is central to the quasi-continuum reduction of field theories. Further,
we derive the homogenized equations that govern the behavior of electronic
fields in regions of smooth deformations. Using Fourier analysis, we determine
the far-field solutions for these fields in the presence of local defects, and
subsequently estimate cell-size effects in computed defect energies.
