The structure of ansatz

Returning to the ansatz (3):

    (10)

where and and we specifically use:

    

In these notations, the pairing is:

    (11)

and therefore the vertex is of the form:

    

We have to first act with on , reexpand the result in linear combinations of expressions of the form , and then evaluate:

    

It is useful to consider particular example when there are no ’s, i.e. , i.e. .