Premium
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
Abstract 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.