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Feynman path integral representation for many‐fermion interacting systems
Author(s) -
Calamante F.,
Bochicchio R. C.,
Grinberg H.
Publication year - 1994
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.560490604
Subject(s) - propagator , path integral formulation , feynman diagram , hamiltonian (control theory) , fermion , density matrix , grand canonical ensemble , mathematical physics , physics , coulomb , quantum mechanics , operator (biology) , partition function (quantum field theory) , trace (psycholinguistics) , many body problem , statistical physics , mathematics , quantum , monte carlo method , mathematical optimization , biochemistry , statistics , chemistry , repressor , transcription factor , gene , electron , linguistics , philosophy
A many‐fermion interacting system is investigated within the scenario of the Feynman path integral representation of quantum mechanics. Short‐time propagator algorithms and a basis set, closely related to the coherent states, are used to obtain the many‐body analytic propagator. A second‐quantized Hamiltonian involving a restricted set of two‐body interactions and the whole set of Coulomb interactions are separately and shown to lead to an exact and an approximate propagator, respectively. In the latter case, use of a grand canonical ensemble allows the grand partition function and the density operator matrix to be readily obtained. No further approximations are required in the calculation of the trace of the evolution operator involved in the evaluation of statistical expectation values. © 1994 John Wiley & Sons, Inc.