where N = N B ^ ^ + N a ^ ^ and N B ^ ^ = J + K while the explicit momentum indices are suppressed for the sake of briefness. These quantities are normally ordered, which means that all creation operators are on the left-hand side while all annihilation operators are on the right-hand side in the expectation value. It is straight forward to show that this expectation value vanishes if the amount of Fermion creation and annihilation operators are not equal.