ON THE SCATTERING THEORY OF MASSLESS NELSON MODELS

C. GÉRARD
2002 Reviews in Mathematical Physics  
We study the scattering theory for a class of non-relativistic quantum field theory models describing a confined non-relativistic atom interacting with a massless relativistic bosonic field. We construct invariant spaces H ± c which are defined in terms of propagation properties for large times and which consist of states containing a finite number of bosons in the region {|x| ≥ ct} for t → ±∞. We show the existence of asymptotic fields and we prove that the associated asymptotic CCR
more » ... otic CCR representations preserve the spaces H ± c and induce on these spaces representations of Fock type. For these induced representations, we prove the property of geometric asymptotic completeness, which gives a characterization of the vacuum states in terms of propagation properties. Finally we show that a positive commutator estimate imply the asymptotic completeness property, ie the fact that the vacuum states of the induced representations coincide with the bound states of the Hamiltonian.
doi:10.1142/s0129055x02001508 fatcat:3yofuablbzhbnixz2rchlsm5rm