Renormalizing an initial state

TL;DR

This paper develops a perturbative approach to construct and renormalize initial states in quantum field theory, addressing the often-overlooked aspect of initial conditions and their impact on the evolution of states, especially in cosmological contexts.

Contribution

It introduces a method to define and renormalize initial states perturbatively using Green's functions and renormalization conditions, with applications to inflationary models.

Findings

Perturbative construction of initial states is feasible using Green's functions.

Renormalization conditions fix the form of initial states in quantum field theory.

Application to inflation demonstrates the method's relevance in cosmology.

Abstract

The intricate machinery of perturbative quantum field theory has largely been devoted to the 'dynamical' side of the theory: simple states are evolved in complicated ways. This article begins to address this lopsided treatment. Although it is rarely possible to solve for the eigenstates of an interacting theory exactly, a general state and its evolution can nonetheless be constructed perturbatively in terms of the propagators and structures defined with respect to the free theory. The detailed form of the initial state in this picture is fixed by imposing suitable `renormalization conditions' on the Green's functions. This technique is illustrated with an example drawn from inflation, where the presence of nonrenormalizable operators and where an expansion that naturally couples early times with short distances make the ability to start the theory at a finite initial time especially desirable.