Getting a handle on correlation functions

TL;DR

This paper provides a pedagogical overview of quantum field theory correlation functions, focusing on their structure, complexity, and how symmetries can simplify their analysis.

Contribution

It introduces tools and methods to manage the complexity of n-point correlation functions using symmetry principles in quantum field theory.

Findings

Symmetries help organize and simplify correlation functions.

Tensor decompositions encode physical information efficiently.

Tools are provided for handling complex correlation structures.

Abstract

The central objects in a quantum field theory are its n-point correlation functions and matrix elements. Their structure is determined by Lorentz invariance and leads to tensor decompositions whose Lorentz-invariant coefficient functions encode the physics of the process. For growing n, the complexity of these objects may increase considerably and make it challenging to deal with them. Here we give a pedagogical introduction to the topic and provide some tools to manage this complexity, and we will show how symmetries can be used as organizing principles.