Relativistically covariant formulation of the canonical theory of classical fields II

TL;DR

This paper develops a covariant canonical theory for interacting classical fields on space-like hypersurfaces, deriving an invariant identity that generalizes the Yang-Feldman equation to a classical, relativistically covariant framework.

Contribution

It introduces a covariant canonical formulation for classical fields with interactions, extending the Yang-Feldman equation to a classical, relativistic context.

Findings

Derived an invariant identity under canonical transformations.

Formulated a covariant canonical equation for interacting fields.

Connected the classical theory to the quantum Yang-Feldman equation.

Abstract

A covariant description of the canonical theory for interacting classical fields is developed on a space-like hypersurface. An identity invariant under the canonical transformations is obtained. The identity follows a canonical equation in which the interaction Hamiltonian density genarates a deformation of the space-like hypersurface. The equation just corresponds to the Yang-Feldman equation in the Heisenberg pictures in quantum field theory.