An inverse scattering problem for the Klein-Gordon equation with a classical source in quantum field theory

摘要

An inverse scattering problem for a quantized scalar field Φ obeying a linear Klein-Gordon equation (□ + m~2 + V)Φ = J in R x R~3 is considered, where V is a repulsive external potential and J an external source. We prove that the scattering operator J = J(V, J) associated with Φ uniquely determines V. Assuming that J is of the form J(t,x) = j(t)p(x), (t,x) G R × R~3, we represent p (resp. j) in terms of j (resp. p) and J.