Notes on LSZ, i epsilon Prescriptions and Perturbation Theory, in QFT and Cosmology

TL;DR

This paper reviews the LSZ reduction formula, clarifies the role of i epsilon prescriptions in QFT and cosmology, and discusses unitarity in inflationary models, providing insights into perturbation theory and correlation functions.

Contribution

It clarifies the LSZ argument, explains the origin of i epsilon prescriptions without assuming a free vacuum, and extends the discussion to inflationary cosmology.

Findings

Clarified the LSZ relation between S-matrix and correlation functions.

Explained the origin of i epsilon prescriptions without assuming a free vacuum.

Discussed unitarity and contour deformations in inflationary cosmology.

Abstract

We review the original argument of Lehmann et al (LSZ) that relates the flat space S-matrix to the correlation function of field operators and clarify some confusing issues. Next we discuss the origin of the $i\epsilon$ prescriptions following Weinberg, but without assuming that the vacuum is free at asymptotic times. Then we discuss the corresponding argument in inflationary cosmology, emphasizing that unitarity violating contour deformations are unnecessary.