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“Basis” lie algebra of electronic fock space: Application to evaluation of matrix elements of spin tensor operators
Author(s) -
Panin A. I.
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.560270502
Subject(s) - fock space , tensor operator , algebra over a field , basis (linear algebra) , mathematics , universal enveloping algebra , tensor (intrinsic definition) , pure mathematics , algebra representation , physics , quantum mechanics , mathematical analysis , geometry , spherical harmonics
A new set of generators of the operator algebra over the electronic Fock space is introduced. It is shown that with this set of generators the “basis” Lie algebra can be associated and that the operator algebra of the Fock space is the homomorphic image of the corresponding universal enveloping algebra. The algebraic structure revealed is used for deriving the reduction formulas for the elements of the simplest spin tensor operators between the Gelfand states.