Scattering theory for Klein-Gordon equations with non-positive energy
نویسنده
چکیده
We study the scattering theory for charged Klein-Gordon equations: (∂t − iv(x))2φ(t, x) + (x,Dx)φ(t, x) = 0, φ(0, x) = f0, i−1∂tφ(0, x) = f1, where: (x,Dx) = − ∑ 1≤j,k≤n ( ∂xj − ibj(x) ) a(x) (∂xk − ibk(x)) +m (x), describing a Klein-Gordon field minimally coupled to an external electromagnetic field described by the electric potential v(x) and magnetic potential ~b(x). The flow of the Klein-Gordon equation preserves the energy:
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