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if I want to calculate the generating functional for the free Dirac Field, I have to evaluate a general Gaussian Grassmann integral. The Matrix in the argument of the exponential function is (according to a book) given by:

I don't understand the comment with the minus-sign and the integration by parts. I tried to do this integration, but didn't get the same result.

Could anyone tell me, how this integration works explicitly?

Or is there a mistake in the book and in the last line it should be +m (not -m) ?

Regards,

Mr. Fogg