Sadun L.A., Avron J.E.
ADIABATIC CURVATURE AND THE $S$-MATRIX
(50K, Plain TeX)
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.