  We construct energy independent but non-local potentials above inelastic
thresholds, in terms of Nambu-Bethe-Salpeter wave functions defined in quantum
field theories such as QCD. As an explicit example, we consider NN --> NN + n
pi scattering processes for n=0,1,2,.... We show an existence of
energy-independent coupled channel potentials with a non-relativistic
approximation, where momenta of all particles are small compared with their own
masses. In the case of two-body inelastic scatterings such as Lambda Lambda -->
Lambda Lambda, N Xi, Sigma Sigma, on the other hand, we show that
energy-independent potentials can be constructed without relying on
non-relativistic approximations. We also propose a method to extract these
potentials using time-dependence of general correlation functions.
