Scattering theory for massless Dirac fields with long-range potentials

For a massless Dirac equation in flat spacetime with scalar long-range potential, we define the Dollard-modified wave operators and prove their existence and asymptotic completeness by means of fully time-dependent methods as used by Derezinski and Gerard [Scattering Theory of Classical and Quantum N-Particle Systems, Springer-Verlag, Berlin/New York, 1997]. We also establish some intermediate results that are new and interesting for their own sake: several weak propagation estimates in different cones of the spacetime and the construction of the asymptotic velocity operators P+/-. The spectra of P+/- can be interpreted as the physically admissible values of the speed and direction of propagation of the fields when t -> +/-infinity. We prove that sigma (P+/-) = S-2 or S-2 boolean OR {0}, where the states of zero asymptotic velocity correspond (when they exist) to the bound states of the massless Dirac Hamiltonian. (c) 2005 Elsevier SAS. All rights reserved.