Communications in Mathematical Physics

, Volume 332, Issue 3, pp 1167–1202 | Cite as

A Criterion for Asymptotic Completeness in Local Relativistic QFT

  • Wojciech DybalskiEmail author
  • Christian Gérard


We formulate a generalized concept of asymptotic completeness and show that it holds in any Haag–Kastler quantum field theory with an upper and lower mass gap. It remains valid in the presence of pairs of oppositely charged particles in the vacuum sector, which invalidate the conventional property of asymptotic completeness. Our result can be restated as a criterion characterizing a class of theories with complete particle interpretation in the conventional sense. This criterion is formulated in terms of certain asymptotic observables (Araki–Haag detectors) whose existence, as strong limits of their approximating sequences, is our main technical result. It is proven with the help of a novel propagation estimate, which is also relevant to scattering theory of quantum mechanical dispersive systems.


Neutral Particle Asymptotic Completeness Superselection Sector Main Technical Result Weyl Quantization 
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© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Institut für Theoretische PhysikZurichSwitzerland
  2. 2.Zentrum MathematikTechnische Universität MünchenGarchingGermany
  3. 3.Département de MathématiquesUniversité de Paris XIOrsay CedexFrance

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