Inversions of the Effective Action in Condensed Matter Models

The quantum effective action may be used to invert information from phenomena, either measured or ideal, to the microscopic Lagrangian. As an example of this procedure the lattice composition of a solid can be determined in principle from desired critical phenomena. Also, the engineering of scattering and optical properties of particular degrees of freedom, and excitations, in terms of the temperature and electro-magnetic fields may be performed.