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Structural signs and carrier completeness of Liouvillian quasiparticle algebras: Dual group invariants for explicit 𝒮 n ‐auxiliary tensor labels via projective mappings applicable to [ A ] n ≤20 NMR spin ensembles
Author(s) -
Temme F. P.
Publication year - 2002
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.10311
Subject(s) - mathematics , group (periodic table) , pure mathematics , lattice (music) , completeness (order theory) , dual (grammatical number) , discrete mathematics , physics , quantum mechanics , mathematical analysis , art , literature , acoustics
Various structural sign aspects of (Liouvillian) dual carrier spaces are examined under (quasiparticle [QP]) dual group projective mappings and Lie‐based algebras. The completeness of these superboson mappings and the nature of the correlation between the two distinct spatial QP sets of mappings are demonstrated in a direct Lie algebraic approach as being superior to supergenerator‐based right‐derivation methods. The dual tensorial auxiliary labels of superboson dual carrier mappings are presented in terms of dual group invariants based on democratic recoupling. The 2 n decompositional modeling is utilized for the cardinality of SU (2) × 2 n group invariants (SIs) of (polyhedral) higher‐(2n) [ A ] 2 n : 12 ∼ 2 n ≤ 20 systems and the auxiliary “ v ” sets. Use of (augmented Weyl) time‐reversal invariance over sets of uniform (democratic) (2 n )‐apical geometric lattice points allows one to treat all the intrinsic (2 i ) < (2 n ) subproblems originating from stepwise substitution of ( Î · Î ) pairs by 1 unities. Use of established 2 n logic provides a ∑ (χ [λ] 1 n) 2 ( n ) model for the fundamental | SI | (2 n ) fterms. PACS : 2.10; 02.20‐a; 33.20 Vq; 33.25 + j. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002