Representing the Vacuum Polarization on de Sitter

TL;DR

This paper demonstrates that a simple, noncovariant representation of vacuum polarization on de Sitter space can be converted into the covariant form without loss of information, improving analysis techniques and addressing general backgrounds.

Contribution

It introduces a closed-form method to convert noncovariant structure functions to covariant ones and offers an improved technique for extracting these functions from diagrams.

Findings

Closed-form conversion procedure established.

Enhanced method for reading structure functions from diagrams.

Discussion on vacuum polarization representation in general metrics.

Abstract

Previous studies of the vacuum polarization on de Sitter have demonstrated that there is a simple, noncovariant representation of it in which the physics is transparent. There is also a cumbersome, covariant representation in which the physics is obscure. Despite being unwieldy, the latter form has a powerful appeal for those who are concerned about de Sitter invariance. We show that nothing is lost by employing the simple, noncovariant representation because there is a closed form procedure for converting its structure functions to those of the covariant representation. We also present a vastly improved technique for reading off the noncovariant structure functions from the primitive diagrams. And we discuss the issue of representing the vacuum polarization for a general metric background.