Canonical Formalism in Special Relativity

TL;DR

This paper develops a covariant Hamiltonian framework for special relativity, connecting field variables with Poincaré generators and generalizing world line conditions across different relativistic dynamics forms.

Contribution

It introduces a covariant Hamiltonian formalism in special relativity and generalizes Currie's world line conditions for any relativistic dynamics form.

Findings

Derived explicit relations between covariant field variables and Fourier variables.

Transformed Hamiltonian formalism to obtain Poincaré generators for any relativistic dynamics.

Generalized world line conditions to all forms of relativistic dynamics.

Abstract

A covariant Hamiltonian description was introduced in the dynamics of charges and electromagnetic interaction. By a canonical transformation this Hamiltonian formalism was transformed to obtain the Dirac generators for any form of relativistic dynamics, as coefficients of a first degree polynomial in the ten translation and rotation velocities of the Poincar\'e transformation. The Currie's world line conditions were generalized to any form of the dynamics. The explicit relation between the covariant field variables and the more usual 3-dimensional Fourier variables was derived.