Questions tagged [grassmann-numbers]

I have two questions on Grassmann numbers. In particular, their naive representation using "huge matrices". Apparently, the anticommutation relations $\{ \xi_i, \xi_j \} = 0$, $\{ \xi_i, \xi^{*}_j \} = 0$ hold for Grassmann numbers, in contrast to…

Let $A$ be an antisymmetric matrix. Usually, one proves that for a Grassmann integral of the type, $$\int d\psi d\theta \exp( \psi^T A \theta) = \det(A)$$ where $\psi$ and $\theta$ are vectors of Grassmann variables. I have a different problem which…

In Appendix 2B of the CFT yellow book by Francesco et al, the authors introduced two types of Grassmann Gaussian integrals (the $\theta$'s below are generators of a Grassmann algebra): The "real" one $$ I = \int d\theta_1 \cdots d\theta_n…