Department of Physics, University of Washington,
Seattle, Washington 98195-1560
Dynamic processes are related to ground state properties of many-body quantum systems and also to equilibrium critical phenomena. For example, KPZ type growth of a line interface, describes also the ground state properties of interacting electrons running around a ring in the presence of an electric field, and the equilibrium crystal shape at a facet-ridge endpoint. These equivalences suggest we search for generalizations of conformal field theory to classify scaling properties of time evolution operators in D=1+1 dimensions: for Tomonaga-Luttinger liquids and conformal field theory the ``dynamic critical exponent" is equal to z=1; for non-relativistic electrons and EW type growth z=2; and for KPZ type growth z=1.5. Phase diagrams of specific models contain all four dynamic universality classes and the crossover scaling is such that z>1 typically decreases. The z-theorem explains this. The crossover from EW to KPZ type growth, and from isotropic to directed percolation are examples.