# Tree-level correlations in the strong field regime

## TL;DR

This paper derives a tree-level framework for calculating correlation functions of local observables in quantum field theory's strong field regime, emphasizing initial state fluctuations and classical solutions.

## Contribution

It provides a general expression for correlation functions at tree level using classical solutions and derivatives, with a novel graphical tree representation.

## Key findings

- Correlation functions arise from initial state fluctuations at tree level.
- The correlation functions can be expressed as sums over labeled trees.
- Additional tree-level terms appear for higher-order correlations beyond the strong field approximation.

## Abstract

We consider the correlation function of an arbitrary number of local observables in quantum field theory. We show that, at tree level in the strong field regime, these correlations arise solely from fluctuations in the initial state. We obtain the general expression of these correlation functions in terms of the classical solution of the field equation of motion and its derivatives with respect to its initial conditions, that can be arranged graphically as the sum of labeled trees where the nodes are the individual observables, and the links are pairs of derivatives acting on them. For 3-point (and higher) correlation functions, there are additional tree-level terms beyond from the strong field approximation, generated throughout the evolution of the system.