Field theory for athermal solids

Amorphous solids composed of macroscopic constituents, like granular media, foams, and emulsions, can be considered as zero temperature systems. Long ago, Edwards proposed that such systems could be treated by statistical mechanical methods by taking a flat average over all metastable states. Despite its attractive parsimony, this hypothesis has remained controversial and has led to conflicting results. I will present some new ideas that remove the ambiguity in Edwards' approach and make it a constructive, feasible route to derive macroscopic equations of state and field equations for athermal systems. In particular, I will show how shear strain can be included as a control parameter, explain the effect of preparation protocol, and show the utility of the renormalization group in this context.