Scattering theory for the Klein-Gordon equation with non-positive energy
Talk by Christian Gérard
Date: 17.03.11 Time: 14.00 - 15.00 Room: ETH HIT E 41.1
Abstract: we discuss the scattering theory for Klein-Gordon equations in the case the conserved energy is not positive definite. The typical example is the Klein-Gordon equation minimally coupled to an external electrostatic potential V, when the potential is sufficiently large.It follows that the generator of the evolution may have complex eigenvalues and the Klein-Gordon evolution cannot be considered as a unitary evolution on a Hilbert space. This phenomenon is usually called the superradiance.
We will describe complete results on scattering theory in the case when the electric potential decays at infinity. The proofs rely on the theory of selfadjoint operators on Krein spaces, and an adaptation of Hilbert space time-dependent methods to the setup of Krein spaces.