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Expansion and completeness theorems for operator manifolds
Author(s) -
Dalgaard Esper
Publication year - 1979
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.560150204
Subject(s) - completeness (order theory) , propagator , operator (biology) , mathematics , basis (linear algebra) , excitation , excited state , pure mathematics , algebra over a field , mathematical physics , physics , mathematical analysis , quantum mechanics , chemistry , biochemistry , geometry , repressor , transcription factor , gene
Some expansion and completeness theorems for operator manifolds, which are currently being employed in propagator theory, are derived. It is shown that excitation or ionization operators satisfying the conditions Q Λ † |0〉 = |Λ〉 and Q Λ |0〉 = 0 for general excited states |Λ〉 and reference state |0〉 may be expanded uniquely in particular sets of basis operators. These results are then used to discuss rigorous expressions for fermion propagators.