The only place I found this result is equation 2.1.7 in Ref. 1. But I can't worked it out. I have tried to vary the term $\nabla \phi$ respect to $\delta g^{\mu\nu}$ (I am only try in the case of the action functionally depends on $[g,\phi,\nabla \phi]$), but I am not sure how the generators appeared (the spin tensor contains it), how to swap $\nabla_\mu$ to in front of these terms?
Does anything wrong with that equation?
I guess 'no'. But, if so, how to obtain it?
References:
- L.B. Szabados, On canonical pseudotensors, Sparling's form and Noether currents, Class. Quantum Gravity 9 (1992) 2521. The preprint pdf file is available here.
