Computing path integral with real and Grassmann variables

  • #1
Geigercounter
8
2
Homework Statement
I want to compute the following path integral
Here $w_i(x)$ are functions of the $n$ real variables $x_i$ and $\theta_i$ and $\overline{\theta}_i$ are $n$ independent Grassmann variables.
Relevant Equations
See below.
The first step seems easy: computation of the $\theta$ and $\overline{\theta}$ integrals give


From here, I tried using that But I don't seem to be able to apply this step.

Other ideas I had included writing out the determinant as to then use some kind of partial integration.
Another, similar, idea was to use the fact that
 
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  • #2
Performing the integration exactly for could very well not be possible. You may very well not be able to obtain the exact value even if you were just considering this integral:



Could you clarify what it is you are aiming to achieve exactly? Do we know what the functions are explicitly? Are you wanting to put the integral into some nice form rather than explicitly evaluating it? Could you show us the source of the question?
 
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