L. Fatibene et al., ANOTHER FORMALISM FOR CONSERVED QUANTITIES IN CLASSICAL GAUGE FIELD-THEORIES, Journal of mathematical physics, 35(4), 1994, pp. 1644-1657
Gauge theories coupled with the gravitational field and external matte
r fields are considered and Notherian techniques are used to build the
canonical conserved quantities. Their superpotentials are found and t
he relation between the canonical stress tensor and the Hilbert tensor
is determined. The case of Yang-Mills theories coupled with gravity a
nd scalar matter fields is considered in detail and it is shown that i
n this case the canonical stress tensor and the Hilbert tensor coincid
e.