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I want to simplify:

$\int dp dp' f(p,p') \delta''(p-p')$

where f(p,p') is an unknown function.

How do I deal with the second derivative of the delta function?

Luke
  • 103
  • it should be $\int f''(p,p)dp$ because:

    $\int f(x)\delta''(x)dx = f''(0)$. The $\delta''(p-p')$ term ensures that you evaluate only on $p=p'$. so you get the above

     – fGDu94 Dec 03 '19 at 12:26

1 Answers1

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You should integrate by parts twice ti shift the derivatives off the delta and on to the function f(p, p'). Doing this, and assuming the boundary terms cannot contribute (they should not saturate the delta function) will leave $$(-1)^2\int dp dp' f''(p, p') \delta(p-p'). $$

Can you finish from here?

lux
  • 805