A new diagrammatic representation for correlation functions in the in-in formalism

TL;DR

This paper introduces an alternative, local diagrammatic method for calculating correlation functions in the in-in formalism, simplifying the process and reducing the number of diagrams, with particular relevance to cosmological applications.

Contribution

It presents a novel diagrammatic approach based on retarded propagators and iterative solutions, making calculations more local and physically interpretable, and reducing diagram complexity.

Findings

Equivalent results to standard methods

Fewer diagrams needed in calculations

Enhanced suitability for cosmological applications

Abstract

In this paper we provide an alternative method to compute correlation functions in the in-in formalism, with a modified set of Feynman rules to compute loop corrections. The diagrammatic expansion is based on an iterative solution of the equation of motion for the quantum operators with only retarded propagators, which makes each diagram intrinsically local (whereas in the standard case locality is the result of several cancellations) and endowed with a straightforward physical interpretation. While the final result is strictly equivalent, as a bonus the formulation presented here also contains less graphs than other diagrammatic approaches to in-in correlation functions. Our method is particularly suitable for applications to cosmology.