The $:\phi^4_4:$ quantum field theory, I. Wave operator, holomorphity and Wick kernel

TL;DR

This paper constructs the Wick kernel for the interacting quantum field in four-dimensional spacetime using complex structures and wave operators, linking it to classical solutions of the nonlinear Klein-Gordon equation.

Contribution

It introduces a novel approach to defining the Wick kernel in 4D quantum field theory via classical wave operators and complex structures, highlighting its properties and classical correspondence.

Findings

Wick kernel defined using wave operators and complex structure

Diagonal of Wick kernel corresponds to classical solutions

Properties of the Wick kernel analyzed in the context of $u^4_4$ interaction

Abstract

With the help of the complex structure and the wave operator of the nonlinear classical Klein-Gordon equation with the interaction $u^4_4$ we define the Wick kernel of the interacting quantum field in four-dimensional space-time and consider its properties. In particular, the diagonal of this Wick kernel is (real) solutions of the classical nonlinear Klein-Gordon equation with the interaction $u^4_4.$