Existence of the Bogoliubov S(g) operator for the $(:ϕ^4:)_2$ quantum field theory
We prove the existence of the Bogoliubov S(g) operator for the $(:ϕ^4:)_2$ quantum field theory for coupling functions $g$ of compact support in space and time. The construction is nonperturbative and relies on a theorem of Kisyński. It implies almost automatically the properties of unitarity and causality for disjoint supports in the time variable.
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