Asymptotic completeness in nonrelativistic quantum field theory
The contents of the invited lecture to the XXIX Symposium on Mathematical Physics, Toruń, 3-6 December, 1996. Two simple nonrelativistic quantum field theory models of mathematical scattering theory are considered. The goal is to show asymptotic completeness for both models. The first model is called by the author ``standard model of nonrelativistic matter''. It describes a system of particles which are divided into species and are identical within each species, subject to either bosonic or fermionic statistics. The model preserves the number of particles of each species and is Galilean-covariant. The theorem of asymptotic completeness of the system is stated whose proof can be reduced to the corresponding theorem for \(N\)-body Schrödinger operators. The detail consideration is expected to appear in Rev. Math. Phys. The second model sometimes called Pauli-Fierz Hamiltonian describes a small spatially confined system such as an atom or impurity interacting with free bosons (radiation, phonons, etc.). The model avoids the infra-red problem and is not translation-invariant but does not preserve the number of particles. The proof of asymptotic completeness for the model is being prepared for publication.
nonrelativistic quantum field theory models
standard model of nonrelativistic matter
scientific article; zbMATH DE number 1158132