0
$\begingroup$

enter image description here

I've been working on this problem set for a little bit now and I've finally made it to the last question. I'm now left with this monster and I don't quite understand where to proceed. All the previous problems were much simpler functionals and their derivatives were easy to calculate.

With this functional I don't really understand how I am supposed to treat $\Delta(x-y)$ when using the definition of the functional derivative to caclulate $\large\frac{\delta\mathcal{Z_0}[J]}{\delta J(\mathcal{z_1})}$. Any sort of clarification about that specific delta function or any trick that I could use to calculate this would be much appreciated.

$\endgroup$
  • $\begingroup$ Treat it as an ordinary function and take derivative. $\endgroup$ – MEDVIS Dec 19 '14 at 8:47
1
$\begingroup$

Instead of you, I would study in terms of $H$ the difference $Z_0 (J+H) - Z_0 (J)$, because the term in $H$ that would appear would be exactly the differential at $J$ evaluated at $H$, and you'll be done.

$\endgroup$
  • $\begingroup$ I was actually able to fiddle with it for a bit and figured out where I was going wrong with my thought process. Thanks for the input though! $\endgroup$ – Seenathin Dec 19 '14 at 9:06

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.