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I read the chapter "Anticommuting Numbers" by Peskin & Schröder (page 299) about Grassmann Numbers and now I would like to prove

[tex]\int d \bar{\theta}_1 d \theta_1 ... d \bar{\theta}_N d \theta_N e^{-\bar{\theta} A \theta} = det A [/tex]

[tex]\theta_i [/tex] are complex Grassmann Numbers.

[tex] \bar{\theta}_i[/tex] are the complex conjugates of [tex] \theta_i [/tex].

In Peskin & Schröder there is no derivation at all, so I tried to find it via google.

In lecture notes I found

But I don't understand, how the author expanded to get the first line. How he used the general ordering result and permutations to get the rest.

Could anybody explain that or refer to a website, with an explicit example, for maybe N=2 ?

Regards,

Mr. Fogg