# Least action principle for Lorentz force in dilaton-Maxwell electrodynamics

## TL;DR

This paper develops a least action principle for test particles in dilaton-Maxwell backgrounds, deriving a generalized Lorentz force and identifying energy integrals for particle dynamics in symmetric electrostatic fields.

## Contribution

It introduces a new least action formulation and explicit Lorentz force generalization for dilaton-Maxwell theories, including energy conservation in stationary backgrounds.

## Key findings

- Derived the generalized Lorentz force for dilaton-Maxwell electrodynamics.
- Established an energy integral for stationary backgrounds.
- Solved radial dynamics in spherically symmetric electrostatic fields.

## Abstract

The least action principle is established for the dynamics of a test particle in a dilaton-Maxwell background. These dynamics and background are invariant under the action of the dilatation transformation; explicit form of the corresponding generalization of the Lorentz force is established for the considered model. On a stationary background, we have found the integral of motion of the energy type. This integral is used to resolve the radial dynamics of test particles in a spherically symmetric electrostatic background.