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selfAdjoint

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## Main Question or Discussion Point

I am going again over Polchinski's excercises, trying to work them and using http://schwinger.harvard.edu/~headrick/polchinski.html [Broken] when I get stuck. In problem 2.1, P. wants us to show that

[tex]\partial \bar{\partial} ln \vert z \vert^2 = 2 \pi \delta^2(z,\bar{z}) [/tex]

and Headrick, introducing a test function f(z) under the integral sign,

[tex] \int_R d^2z \partial \bar{\partial} ln \vert z \vert^2 f(z) [/tex]

eventually gets

[tex] \partial \bar{\partial} ln \vert z \vert^2 = 2 \pi f(0) [/tex]

Can anybody spell out for me how this arbitrary f(o) is the delta function?

[tex]\partial \bar{\partial} ln \vert z \vert^2 = 2 \pi \delta^2(z,\bar{z}) [/tex]

and Headrick, introducing a test function f(z) under the integral sign,

[tex] \int_R d^2z \partial \bar{\partial} ln \vert z \vert^2 f(z) [/tex]

eventually gets

[tex] \partial \bar{\partial} ln \vert z \vert^2 = 2 \pi f(0) [/tex]

Can anybody spell out for me how this arbitrary f(o) is the delta function?

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