A Second derivative of Heaviside step function

abhinavabhatt
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Identifying Klein Gordon propagator as Green's Function
In QFT by peskin scroeder page 30 the action of Klein Gordon Operator on propagator
(∂2+m2)DR(x-y)=∂2θ(x0-y0)...

how to compute this
∂2θ(x0-y0)?
 

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First derivative is delta function. The second derivative ##\delta'(x)## has property
\int \delta'(x) f(x) dx = -f'(0)
 
Thanks for the answer.
 
Note that Peskin and Schroeder write in fact the correct equation, i.e.,
$$(\Box+m^2) D_{R}(x-y)=-\mathrm{i} \delta^{(4)}(x-y).$$
Since by definition ##D_R(x-y) \propto \Theta(x^0-y^0)## this function is the retarded Green's function of the Klein-Gordon operator (modulo the usual conventional factor ##-\mathrm{i}## on the right-hand side).
 

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