Scattering theory for massless Dirac fields with long-range potentials (Q2487978)

The author studies a massless Dirac equation in flat space time with scalar long range potential and defines a Dollard modified wave operator. Existence and asymptotic completeness are established. Weak propagation estimates and asymptotic velocity operators are obtained. There are analytic difficulties involved in the absence of mass; the Dirac Hamiltonians are not invertible and there is a singularity at the origin of the scalar symbol. The low energies must be cut-off in the course of the computations. Weak propagation estimates are used to construct asymptotic velocity operators and to study their spectra.