  In this work a periodic crystal with point defects is described in the
framework of linear response theory for broken symmetry states using
correlation functions and Zwanzig-Mori equations. The main results are
microscopic expressions for the elastic constants and for the coarse-grained
density, point-defect density, and displacement field, which are valid in real
crystals, where vacancies and interstitials are present. The coarse-grained
density field differs from the small wave vector limit of the microscopic
density. In the long wavelength limit, we recover the phenomenological
description of elasticity theory including the defect density.
