- #1
QFT1995
- 30
- 1
I'm can't seem to figure out how to functionally differentiate a functional such as [tex]Z(J)= e^{\frac{i}{2} \int \mathrm{d}^4y \int \mathrm{d}^4x J(y) G_F (x-y) J(x)} [/tex]
with respect to [itex]J(x) [/itex]. I know the answer is
[tex]\frac{\delta Z(J)}{\delta J(x)}= -i \int \mathrm{d}^4y J(y) G(x-y) [/tex]
but I'm struggling to calculate it.
with respect to [itex]J(x) [/itex]. I know the answer is
[tex]\frac{\delta Z(J)}{\delta J(x)}= -i \int \mathrm{d}^4y J(y) G(x-y) [/tex]
but I'm struggling to calculate it.