# Weak adiabatic limit in quantum field theories with massless particles

January 30, 2018

We construct the Wightman and Green functions in a large class of models of
perturbative QFT in the four-dimensional Minkowski space in the Epstein-Glaser
framework. To this end we prove the existence of the weak adiabatic limit,
generalizing the results due to Blanchard and Seneor. Our proof is valid under
the assumption that the time-ordered products satisfy certain normalization
condition. We show that this normalization condition may be imposed in all
models with interaction vertices of canonical dimension 4 as well as in all
models with interaction vertices of canonical dimension 3 provided each of them
contains at least one massive field. Moreover, we prove that it is compatible
with all the standard normalization conditions which are usually imposed on the
time-ordered products. The result applies, for example, to quantum
electrodynamics and non-abelian Yang-Mills theories.

Keywords:

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