Quantizing the conjugate operator to adjoint operator

[geoduck]

If you have the product of two Grassman numbers C=AB, and take the conjugate, should it be C*=A*B*, or C*=B*A*?

The general rule for operators, whether they are Grassman operators (like the Fermion field operator) or the Bose field operator, I think is (AB)^dagger=B^dagger A^dagger.

This seems to suggest C* should be defined as B*A* for Grassman numbers, so when you quantize to Grassman operators, you get the right definition. Is this right?

 

[dextercioby]

By the convention used in physics (Henneaux &Teitelboim's book), involution on a Grassmann algebra follows the quantum prescription:

$$(AB)^* = B^* A^*$$