Super-operator formalism

In order to express Eq. (50) in a more compact form, it is useful to introduce the super-operator formalism (Pickup and Goscinski, 1973 Goscinski and Lukman, 1970). The time-independent operators are construed as elements in a super-operator space with a binary product... 

According to Eqs. (41) and (34) the static self energy (oo) is given by the primary block of the matrix of Eq. (33) minus its zeroth order part. An explicit expression can be found with the help of the super-operator formalism and using the definition of the extended states (47) ... 

The abstract formalism introduced in this chapter builds the fundament of the theory of extended two-particle Green s functions. Our approach is very general in order to allow for a unified treatment of the different species of extended Green s functions discussed in the main part of this paper. Since the discussed propagators can be applied to a wide variety of physical situations, the emphasis of this chapter lies on the unifying mathematical structure. The formalism is developed simultaneously for (projectile) particles of fermionic and bosonic character. We will define the general extended states which serve to define the primary or model space of the extended Green s functions. We also define the /.j-product under which the previously defined extended states fulfil peculiar orthonormality conditions. Finally we introduce a canonical extension of common Fock-space operators and super-operators to the space of the extended states. 

At about the same time that the CRAY was moved to ULCC, a CYBER 205 was installed at the Manchester Regional Centre (UMRCC), and so, formally at least, by 1983 very adequate super-computing resources were available to the quantum chemical community on a peer-review basis, analogous to the previous provision via SERC central facilities. There was some delay in the CYBER 205 becoming suitably operational, and, in practice, it did not find the same favour with the computational chemistry community in the UK, as... 

---