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Quantizing the conjugate operator to adjoint operator

  1. Nov 12, 2014 #1
    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?
  2. jcsd
  3. Nov 12, 2014 #2


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

    [tex] (AB)^* = B^* A^* [/tex]
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