As I read in my quantum mechanics book the delta function is sometimes called the sampling function because it samples the value of the function at one point.(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\int {\delta (x - x')} f(x')dx' = f(x)[/tex]

But then I opened a quantum field book and I found equations like that:

[tex]\phi (x) = \frac{1}{{(2\pi )^{3/2} }}\int {d^4 p\delta (p^2 } - m^2 )A(p)e^{ - ip \cdot x} [/tex]

[tex](\partial _\nu \partial ^\nu + m^2 )\phi (x) = \frac{1}{{(2\pi )^{3/2} }}\int {d^4 p( - p^2 } + m^2 )\delta (p^2 - m^2 )A(p)e^{ - ip \cdot x} [/tex]

Can someone explain me what the delta function does here? What it is sampling? How these equations work?

thank you

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# Dirac function

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