I’m doing some calculations with Dirac delta function and I don’t know if I can split te function. I’ll show in a picture
Edit1: The integral I was talking about is: $$\int \mathrm{d^4}{p}\,\mathrm{d^4}{q}\,\mathrm{d^4}{w}\,\mathrm{d^4}{\gamma}\,\phi(p)\phi(q)\phi(w)\phi(\gamma){\delta (p+q+w+{\gamma)}}$$
Short answer: no, I really don't think so. Your $\delta$ cares about whether $p+q+w+\gamma$ is $0$, and you can't really separate that into conditions on each of the variables by themselves (or in smaller combinations) in any nice way.