Convert Grassmann numbers to real numbers

Question

We know Grassmann numbers are complex numbers. Hence Grassmann integrals are also complex. How can we convert a Grassmann integral into real one, ie is there any transformation of converting complex Grassmann numbers to real grassmann numbers?

Answer 1

Comments to the question (v3):

1. A Grassmann-odd number is not a complex number. It is a complex supernumber $z=x+iy$, which can be decomposed in real and imaginary supernumbers, cf. e.g. this and this Phys.SE posts.

2. The Berezin integral $\int\! d\theta~f(\theta)$ over supernumbers is an ordinary complex number $c=a+ib\in\mathbb{C}$, which can be decomposed in real and imaginary numbers.