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The particle‐hole component of the 2‐particle green function—its relation to the canonical particle‐hole states and its N‐representability
Author(s) -
Larson Everett G.,
Day Orville W.
Publication year - 2009
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560050882
Subject(s) - particle (ecology) , operator (biology) , physics , projection (relational algebra) , function (biology) , excited state , space (punctuation) , ground state , green's function , quantum mechanics , mathematical physics , classical mechanics , mathematics , chemistry , biochemistry , oceanography , philosophy , algorithm , evolutionary biology , biology , linguistics , repressor , transcription factor , gene , geology
The relation between the 2‐particle Green function and the projections of the excited states onto the particle‐hole space of the ground state of a fermion system is derived for the case in which the spectrum of the Green function is totally discrete. From this relation, the conditions for the N ‐representability of the 2‐particle Green function are obtained, as is an explicit representation of the projection operator for the particle‐hole space. The projection operator for the 2‐particle‐2‐hole space is also presented.