Resolvent, Brillouin-Wigner

Many-Body Brillouin-Wigner Theories Development and Prospects By introducing the Brillouin-Wigner resolvent... 

If we compare the Brillouin-Wigner resolvent for the ground state given in Eq. 2.23... 

This should be compared with the Brillouin-Wigner resolvent (1.15) which for the ground state takes the form... 

To make further progress, we must now introduce the Brillouin-Wigner resolvent. 

The Brillouin-Wigner resolvent In Brillouin-Wigner perturbation theory the resolvent is defined as follows ... 

Brillouin-Wigner Methods for Many-Body Systems we can write the Brillouin-Wigner resolvent as (2.118) =... 

Elimination of the size-extensivity error in the MRBWCC theory was suggested by Hubac and Wilson [68]. The Brillouin-Wigner perturbation theory has been known notoriously as a method not furnishing size extensivity. There was therefore every reason to believe that the size-extensivity error in MR BWCCSD originated from the use of the Brillouin-Wigner type resolvent (15) instead of the Rayleigh-Schrodinger... 

It can be easily shown that Bq, the Brillouin-Wigner type propagator, has the same eigenfunctions as The resolvent can, therefore, be written in the sum-over-states form... 

Generalized Brillouin-Wigner perturbation theory is based on a resolvent of the form... 

The effective Hamiltonian operator (2.88) in Brillouin-Wigner perturbation theory can be written in terms of the resolvent defined in eq. (2.111) in the form... 

An alternative approach, which we shall follow in this work, is to solve eqs. (4.145) and (4.146), which define the much simpler Brillouin-Wigner scheme, and introduce a correction term for the non-linear effects. The following identity relates the Brillouin-Wigner and the Rayleigh-Schrodinger resolvent denominators [17,18,74]... 

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