The minimum energy state

TL;DR

This paper introduces a framework for analyzing the minimum energy state of a quantum field with a time-evolving expectation value, deriving relations between n-point functions, equations of motion, and renormalization in the presence of an external field.

Contribution

It provides a novel formulation linking the minimum energy state with time-dependent expectation values and derives key equations and renormalization procedures for interacting fields.

Findings

Derived relations between n-point functions and external fields.

Established equations of motion for the state.

Identified renormalization counterterms at first order.

Abstract

We define the minimum energy state while the expectation value of the field, evolves in time. We obtain the relation between the n-point functions in such a state, and the external field for all the moments. We obtain an equation of motion and the renormalization counterterms for the external field in the first order of interaction.