Existence of the Bogoliubov S(g) operator for the $(:\phi^4:)_2$ quantum field theory

TL;DR

This paper proves the existence of the Bogoliubov S(g) operator in the nonperturbative setting of the $(:\phi^4:)_2$ quantum field theory, ensuring unitarity and causality for localized interactions.

Contribution

It establishes a nonperturbative proof of the Bogoliubov S(g) operator's existence for $(:\phi^4:)_2$ theory using Kisyński's theorem, with implications for unitarity and causality.

Findings

Existence of the Bogoliubov S(g) operator proven.

Operator construction is nonperturbative.

Unitarity and causality properties are confirmed.

Abstract

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