A universal concept of asymptotic completeness in non-relativistic QED

• Applicant: Professor Dr. Wojciech Dybalski
• Subject Area: Mathematics
• Term: from 2012 to 2013
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 213105674

• Final Report Year: 2014

Final Report Abstract

The project under report concerned scattering of particles in quantum field theory, especially infrared problems and the problem of complete particle interpretation (asymptotic completeness). A number of results have been obtained, both on the side of relativistic and non-relativistic quantum field theory. They concern mostly the construction of scattering states, the problem of existence of asymptotic observables and the relations between these two concepts. Transfer of methods from non-relativistic to relativistic quantum field theory provided new, unexpected insights into the asymptotic dynamics of relativistic systems. This new promising research direction will be pursued in a future project.

Publications

• The translation invariant massive Nelson model: III. Asymptotic completeness below the two-boson threshold
  W. Dybalski and J.S Møller
  
• A criterion for asymptotic completeness in local relativistic QFT. Commun. Math. Phys.
  W. Dybalski and C. Gérard
  (See online at https://doi.org/10.1007/s00220-014-2069-y)
• Coulomb scattering in the massless Nelson model I. Foundations of two-electron scattering. J. Stat. Phys. 154, (2014) 543–587
  W. Dybalski and A. Pizzo
  (See online at https://doi.org/10.1007/s10955-013-0857-y)