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Consistent propagator approximations
Author(s) -
Weiner Brian
Publication year - 1985
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.560280106
Subject(s) - propagator , generalization , hilbert space , fock space , representation (politics) , mathematics , context (archaeology) , space (punctuation) , property (philosophy) , mathematical physics , quantum mechanics , physics , pure mathematics , mathematical analysis , computer science , paleontology , philosophy , epistemology , politics , political science , law , biology , operating system
A propagator approximation scheme is presented in the context of an abstract*‐algebra approach. The representation theory of such algebras is shown to play a crucial role in the definition of consistent approximations, i.e., approximate propagators based on model time evolutions and states. This procedure places superoperator methods of approximation on a sound Hilbert space footing. A generalization of the Fock vacuum property is introduced which leads to a simplification in the form of the model propagators. Finally a concrete example is considered that fulfills the conditions developed in this article showing that a consistent approximation to the electron propagator results in the Hartree–Fock–Boguliubov equations.