Genuine covariant description of Hamiltonian dynamics

TL;DR

This paper reviews the covariant Hamiltonian dynamics framework and applies it to various models including the harmonic oscillator, Rovelli's model, and SO(3,1) BF theories, highlighting its versatility.

Contribution

It provides a comprehensive covariant Hamiltonian formulation and demonstrates its application to multiple physical models, extending previous approaches.

Findings

Unified covariant description of Hamiltonian dynamics.

Application to non-relativistic and relativistic models.

Insights into gauge theories like SO(3,1) BF theories.

Abstract

After reviewing the covariant description of Hamiltonian dynamics, some applications are done to the non-relativistic isotropic three-dimensional harmonic oscillator, Rovelli's model, and SO(3,1) BF theories.