Interactions in Crystals by a Lagrangian Approach

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9712885 Nelson The senior PI, in recent years, has been involved in (a) the development of a Lagrangian formulation of long wavelength phenomena in dielectric crystals, (b) using this formulation to derive and elucidate high-order nonlinear interactions and correcting widely held long standing misconceptions in classical theories and (c) incorporation of magnetic phenomena in his formulation using Grassmann algebra of anticommuting variables. This grant continues to support his work following a string of successes in the previous award. This grant also includes work on a generalized energy conservation law and a new Poynting vector, followed by application to the properties of an optical soliton. %%% This senior PI is well known for his contributions to Laser Physics. In this renewal grant, he continues his work on a sophisticated mathematical formulation of electromagnetic wave propagation in an insulating material. In this renewal he specifically wants to generalize the formulation to include magnetic properties of materials. ***