# Exponent rule for Grassmann numbers

I would like to ask if the following statement is legit for the Grassmann numbers $\eta^*,\xi_1,\xi_2,\xi_3$ and real parameters $A,B$ and $C$?

$$e^{A \eta^*\xi_1} e^{B \eta^*\xi_2}e^{C \eta^*\xi_3} = e^{A \eta^*\xi_1 + B \eta^*\xi_2 + C \eta^*\xi_3}.$$

My thought way this should hold was

$$e^{A \eta^*\xi_1} e^{B \eta^*\xi_2}e^{C \eta^*\xi_3} = (1+ A \eta^*\xi_1)(1+ B \eta^*\xi_2)(1+ C \eta^*\xi_3)$$$$= 1 + \eta^*(A\xi_1 + B\xi_2 + C\xi_3) = e^{A \eta^*\xi_1 + B \eta^*\xi_2 + C \eta^*\xi_3}.$$

• Hey! Have you found out the answer? – user3237992 Apr 30 at 20:00