ADIABATIC CURVATURE AND THE $S$-MATRIX (50K, Plain TeX) Dec 6, 95
Abstract. We study the relation of the adiabatic curvature associated to scattering states and the scattering matrix. We show that there cannot be any formula relating the two locally. However, the first Chern number, which is proportional to the integral of the curvature, {\it can} be computed by integrating a 3-form constructed from the $S$-matrix. Similar formulas relate higher Chern classes to integrals of higher degree forms constructed from scattering data. We show that level crossings of the on-shell $S$-matrix can be assigned an index so that the first Chern number of the scattering states is the sum of the indices. We construct an example which is the natural scattering analog of Berry's spin 1/2 Hamiltonian.