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

We present the covariant Hamiltonian representation of Noether’s theorem and its application to Yang-Mills gauge theory. As the starting point, we re-formulate our previous presentation of the canonical Hamiltonian derivation of Noether’s theorem, distinguishing admissible canonical transformations from symmetries of a specified Hamiltonian. The Noether currents of U(1) and U(N) gauge theories, and their restriction to SU(N), are derived from the respective infinitesimal generating functions of the pertinent symmetry transformations. The resulting conservation relations are distinguished from the complete field equations, which require the chosen kinetic Hamiltonian and a variational treatment of the antisymmetric gauge momenta.