Intensive structure of Heisenburg supergenerator algebras over {v} SU2 dual carrier subspaces in Liouville NMR formalisms: Superbosons as unit tensor superoperators

Time-reversal-based scalar invariants as (Lie Algebraic) group measures: a structured overview of generalised democratic-recoupled, uniform non-Abelian [AX]n NMR spin systems, as abstract chain networks

“…to that of analogous isochronous multispin system. The quantal physics of the former also necessitate some discussion of their relationship to boson (superboson) quasiparticle dual group mapping [8,9]. On utilising the Liouville operatorL ½Ĥ; À (specifically over fjkqviig fT kq ðvÞg integer rank tensorial operator bases [10-12]) to describe evolution processes, certain important quantum physics questions arise.…”

“…With the extensive recent development of cluster-based nanoscience, it is timely to re-examine the impact of theoretical physics concepts on a range of ½AX n type (automorphic) NMR spin systems [5][6][7], whether under even (2n), or odd (2n + 1) indices. Naturally such studies are equally important in the realm of uniform sub-rank (dual) tensorial sets, and their completeness [8,9] as (e.g.) operatorbases of the Liouville equation.…”

“…To illustrate the general NMR significance of the work reported here and to describe the various formalisms involved, brief informative overviews of various pertinent NMR subtopics are given in the initial paragraphs. Naturally these include the following topics: the role of time-reversal invariance in group invariants [4], the nature of both democratic recoupling and tensorial properties in NMR, and (as a comment in Section 2) several ideas associated with quasiparticle carrier space [9] properties of Liouville space; essentially in the context of democratic recoupling [3]. A brief introduction to multipole densityoperator methods [10][11][12] in various post-1976 formalisms pertinent to NMR spin dynamics is included in Section 3 for completeness.…”

“…For reasons based on their specific inherent quantum physics interest (and their previous neglect by the NMR community), we focus on uniform multispin systems described in terms of (multipole) tensorial formalisms [12]. The latter involve the use of (operator)bases involving uniform subrankbased auxiliary labels [9,12,14]. To illustrate the general NMR significance of the work reported here and to describe the various formalisms involved, brief informative overviews of various pertinent NMR subtopics are given in the initial paragraphs.…”

“…operatorbases of the Liouville equation. To appreciate in a systematic way the origin of the properties exhibited by these uniform sub-rank spin systems, one needs to consider their scalar invariants [1,4], parity [2], dual projective [5][6][7][8][9][10][11] and/or recoupling [10,12] properties. The nature of many-body interactions [3, 8,13] implicit in democratic recoupling makes a significant impact on our specific understanding of both NMR evolution and relaxation processes [12, 14,15] once uniform sub-rank multispin cluster systems are considered.…”