# Covariant Brackets for Particles and Fields

## TL;DR

This paper introduces a geometric covariant framework for relativistic particle and field dynamics, utilizing Peierls brackets via bivector fields on solution spaces, with illustrative examples demonstrating the approach.

## Contribution

It presents a novel geometric method to realize Peierls brackets covariantly using bivector fields on the solution space of Euler-Lagrange equations.

## Key findings

- Provides a covariant geometric formulation of dynamics.
- Demonstrates the method with relevant examples.
- Establishes a link between brackets and bivector fields.

## Abstract

A geometrical approach to the covariant formulation of the dynamics of relativistic systems is introduced. A realization of Peierls brackets by means of a bivector field over the space of solutions of the Euler-Lagrange equations of a variational principle is presented. The method is illustrated with some relevant examples.