General Symmetry-Preserving Pair Creation Operators

MORE GENERAL SYMMETRY-PRESERVING PAIR CREATION OPERATORS 

We next turn to the question of whether the total spin operator commutes with Wj v In Ref. [8] it is shown that the components of the total spin operator can be expressed in second-quantized form by means of the relationships  

However, W can be rewritten so that each of the terms in the summation will have the form (h]h- + bjbt). To do this, we notice that since the sum in equation (74) runs over all m values, it will be unchanged if we interchange m and — m in the first term in the round brackets. Thus we can write 

In this form, it is easy to see from equation (77) that the terms in round brackets have the right form to commute with S, and therefore, 

From the argument given above, it can also be seen that the Kramers pair creation operators B t commute with S, since w nl = -JlB v 

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More general symmetry-preserving pair creation operators 197... 

Commutation relations analogous to (42) can also be derived for the more general symmetry-preserving pair creation operators ... 

The example discussed above was the case of spherical symmetry. We can ask whether general symmetry-preserving pair creation operators analogous to Ikj, can be constructed for other types of symmetry. For example, does the operator... 

In addition to the DFT chapters, there are two chapters by John and James Avery the first time a father and son team has published in Advances. In the first, a new and more general type of symmetry-preserving pair creation operator is proposed and extended to cases where orthonormality of orbitals of different configurations cannot be assumed. 

In the present paper, we shall discuss a method for generating many-electron states of a given symmetry using Kramers pair creation operators and other symmetry-preserving pair creation and annihilation operators. We will first develop the formalism for the case where orthonormality between the orbitals of different configurations can be assumed. Afterwards we will extend the method to cases where this orthonormality is lost, so that the method also can be used in generalized Sturmian calculations [11-13] and in valence bond calculations. 

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