Covariant Hamiltonian representation of Noether's theorem and its application to SU(N) gauge theories

TL;DR

This paper develops a covariant Hamiltonian approach to Noether's theorem and applies it to derive the Yang-Mills gauge theory, providing a formalism that links symmetries to conserved currents in gauge theories.

Contribution

It introduces a covariant Hamiltonian formulation of Noether's theorem and applies it to systematically derive U(1) and SU(N) gauge theories from symmetry principles.

Findings

Derived Noether currents for U(1) and SU(N) gauge theories.

Reformulated Hamiltonian derivation of Noether's theorem.

Established a covariant formalism linking symmetries to gauge theories.

Abstract

We present the derivation of the Yang-Mills gauge theory based on the covariant Hamiltonian representation of Noether's theorem. As the starting point, we re-formulate our previous presentation of the canonical Hamiltonian derivation of Noether's theorem. The formalism is then applied to derive the Yang-Mills gauge theory. The Noether currents of U(1) and SU(N) gauge theories are derived from the respective infinitesimal generating functions of the pertinent symmetry transformations which maintain the form of the Hamiltonian.