Scattering for massive scalar fields on Coulomb potentials and Schwarzschild metrics. (English) Zbl 0659.53054

We develop the scattering theory for classical relativistic massive scalar fields propagating in the presence of long-range forces. More specifically we consider (a) the Klein-Gordon equation on Minkowski space with a Coulomb potential and (b) the Klein-Gordon equation for the Schwarzschild metric. In either case our result shows the existence of certain wave operators which compare the full dynamics with a free dynamics modified by a logarithmic phase shift.


53B50 Applications of local differential geometry to the sciences
35Q99 Partial differential equations of mathematical physics and other areas of application
81V10 Electromagnetic interaction; quantum electrodynamics
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