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The projection operators of SU(2) and the Sanibel coefficients
Author(s) -
Zeng ZongHao,
Sun ChiaChung
Publication year - 2009
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.560280810
Subject(s) - homogeneous space , projection (relational algebra) , mathematics , hermitian matrix , unitary state , invariant (physics) , pure mathematics , operator theory , permutation (music) , spectral theorem , algebra over a field , group (periodic table) , mathematical physics , physics , quantum mechanics , algorithm , geometry , political science , acoustics , law
In this article, a group‐theoretical discussion is presented to show that both the spin projection operators proposed by Löwdin and the characteristic operators which have been proposed by Tang and Guo to perform unilarily invariant decomposition of Hermitian operators are in essence equivalent, and they act as two distinct realizations of idempotents of SU(2) to give two different, permutation and unitary, symmetries, respectively. By means of either the spin projection operators or the characteristic operators, the explicit form of the Sanibel coefficients can be obtained directly.