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Scattering theory for the Klein-Gordon equation with non-positive energy

Christian Gerard
(Universite de Paris Sud, Orsay)
Tirsdag, 28 juni, 2011, at 16:15-17:15, in Aud. D3 (1531-215)
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.
Kontaktperson: Erik Skibsted