Nöther formalism for conserved quantities in classical gauge field theories

Gauge theories coupled with the gravitational field and external matter fields are considered and Nötherian techniques are used to build the canonical conserved quantities. Their superpotentials are found and the relation between the canonical stress tensor and the Hilbert tensor is determined. The case of Yang–Mills theories coupled with gravity and scalar matter fields is considered in detail and it is shown that in this case the canonical stress tensor and the Hilbert tensor coincide.