# The non-perturbative structure of the photon and gluon propagators

## TL;DR

This paper investigates the complex non-perturbative features of photon and gluon propagators in QED and QCD, revealing that their decomposition into simple components is often impossible and that gluons exhibit singularities related to confinement, while key symmetries are preserved.

## Contribution

It demonstrates the failure of the longitudinal-transverse decomposition for photon and gluon propagators and identifies singular terms in the gluon propagator linked to confinement, while maintaining Slavnov-Taylor identities.

## Key findings

- Decomposition into longitudinal and transverse components often fails.
- Gluon propagator contains singular terms involving derivatives of delta functions.
- Slavnov-Taylor identity remains valid despite non-perturbative complexities.

## Abstract

The non-perturbative structure of the photon and gluon propagators plays an important role in governing the dynamics of quantum electrodynamics (QED) and quantum chromodynamics (QCD) respectively. Although it is often assumed that these interacting field propagators can be decomposed into longitudinal and transverse components, as for the free case, it turns out that in general this is not possible. Moreover, the non-abelian gauge symmetry of QCD permits the momentum space gluon propagator to contain additional singular terms involving derivatives of $\delta(p)$, the appearance of which is related to confinement. Despite the possibility of the failure of the transverse-longitudinal decomposition for the photon and gluon propagators, and the appearance of singular terms in the gluon propagator, the Slavnov-Taylor identity nevertheless remains preserved.