This award supports a visit by Dr. James D. Stasheff of the University of North Carolina, Chapel Hill, to the University of Sydney, Australia, to work with Dr. Donald Barnes on cohomological methods in mathematical physics. The researchers will address problems in cohomological physics in terms of developing and applying techniques developed by Dr. Stasheff in his earlier research in combination with the relevant and complementary expertise of Dr. Barnes. These techniques fall into two broad categories: homological perturbation theory and the study of higher order homotopy algebraic structure. One approach to quantization is via a special kind of homological perturbation theory. The terms in a perturbed differential can often be interpreted as higher order homotopy structure. Dr. Stasheff identified a Lie algebra version of such structure in several different aspects of mathematical physics. This project will further develop the formal theory of such "strong homotopy Lie algebras" and apply it to the physics. The vast majority of examples of BRST cohomology in physics share the characteristic features of strongly homotopy Lie algebras. This project will address the characterization of BRST cohomology along the characterization of spectral sequence constructors by Dr. Barnes.
