Commutation relations for various tensors

Apart from irreducible tensors (14.30) we can also introduce other operators that are expressed in terms of irreducible tensorial products of second-quantization operators, and establish commutation relations for them. As was shown in [12, 102, 103], using relations of this kind, we can relate standard quantities of the theory, which at first sight seem totally different. Consider the operator 

Rearranging the electron creation operators in the right side of this expression and using the symmetry properties of Clebsch-Gordan coefficients 

The commutation relations between operators (14.40) and (14.42) can be represented in the irreducible tensor form [103, 104] 

Using the anticommutation properties of electron creation and annihilation operators we can establish any necessary commutation relations for their tensorial products. For example, [103] 

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