# Expansion of tree amplitudes for EM and other theories

## TL;DR

This paper derives a general expansion of Einstein-Maxwell tree amplitudes into Yang-Mills amplitudes using differential operators, revealing hidden connections between different theories in quantum field theory.

## Contribution

It introduces a unified method to expand EM amplitudes into YM amplitudes and uncovers shared coefficients across various theory expansions.

## Key findings

- Derived the expansion of EM amplitudes into YM amplitudes.
- Identified shared coefficients among multiple theory expansions.
- Revealed hidden connections between different quantum field theories.

## Abstract

The expansions of tree-level amplitudes for one theory into amplitudes for another theory, which have been studied in various recent literatures, exhibit hidden connections between different theories that are invisible in traditional Lagrangian formulism of quantum field theory. In this paper, the general expansion of tree EM (Einstein-Maxwell) amplitudes into KK basis of tree YM (Yang-Mills) amplitudes have been derived by applying the method based on differential operators. The obtained coefficients are shared by the expansion of tree $\phi^4$ amplitudes into tree BS (bi-adjoint scalar) amplitudes, the expansion of tree sYMS (special Yang-Mills-scalar) amplitudes into tree BS amplitudes, as well the expansion of tree DBI (Dirac-Born-Infeld) amplitudes into tree special extended DBI amplitudes.

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Source: https://tomesphere.com/paper/1907.07857