Professor Battle will continue his work to construct nontrivial quantum field theories. In particular, this project will concentrate on the nonlinear sigma model, a strictly renormalizable asymptotically free theory. His technique of construction will use the relatively new concept of wavelet which he will develop to meet the particular requirements of quantum field theory. Quantum fields are the basic quantities which are thought to be responsible for all the interactions between particles which exist in nature. It is therefore notable that these objects which are essentially mathematical entities, have not been shown to exist. Professor Battle is one of the few mathematical physicists who work in the area of construction of quantum field theories. His project involves the construction of a model theory called the nonlinear sigma model. A side benefit of Battle's work is his use of wavelets in this construction. These objects have turned out to be of use in many other areas of pure and applied mathematics, and Battle has and will continue to contribute toward their development.
