83 research outputs found
From Faddeev-Kulish to LSZ. Towards a non-perturbative description of colliding electrons
In a low energy approximation of the massless Yukawa theory (Nelson model) we
derive a Faddeev-Kulish type formula for the scattering matrix of electrons
and reformulate it in LSZ terms. To this end, we perform a decomposition of the
infrared finite Dollard modifier into clouds of real and virtual photons, whose
infrared divergencies mutually cancel. We point out that in the original work
of Faddeev and Kulish the clouds of real photons are omitted, and consequently
their scattering matrix is ill-defined on the Fock space of free electrons. To
support our observations, we compare our final LSZ expression for with a
rigorous non-perturbative construction due to Pizzo. While our discussion
contains some heuristic steps, they can be formulated as clear-cut mathematical
conjectures.Comment: 12 pages, 1 figur
Asymptotic observables, propagation estimates and the problem of asymptotic completeness in algebraic QFT
We review recent results on the existence of asymptotic observables in
algebraic QFT. The problem of asymptotic completeness is discussed from this
perspective.Comment: 5 pages. Contribution to proceedings of QMath1
A criterion for asymptotic completeness in local relativistic QFT
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.Comment: 29 page
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