# The Lagrange-Poincar\'e equations for interacting Yang-Mills and scalar fields

## TL;DR

This paper derives specialized Lagrange-Poincaré equations for gauge fields interacting with scalar fields, focusing on dynamics within the gauge orbit space using adapted coordinates.

## Contribution

It provides a new formulation of the Lagrange-Poincaré equations tailored for gauge and scalar field interactions, emphasizing the gauge orbit space representation.

## Key findings

- Derived equations describe evolution on gauge orbit space.
- Utilized adapted coordinates for configuration space analysis.
- Neglected group variables to simplify the dynamics.

## Abstract

A special case of the Lagrange-Poincar\'e equations for the gauge field interacting with a scalar field is obtained. For description of the dynamics on the configuration space, the adapted coordinates are used. After neglecting the group variables the obtained equations describe the evolution on the gauge orbit space of the principal fiber bundle which is related to the system under the consideration.