Concept of a veritable osp(1$|$2) super-triangle sum rule with 6-$j^S$ symbols from intrinsic operator techniques: an open problem
| dc.creator | Bréhamet, Lionel | |
| dc.date | 2008-11-13 | |
| dc.date.accessioned | 2026-07-07T10:18:04Z | |
| dc.date.available | 2026-07-07T10:18:04Z | |
| dc.description | Efficiency of intrinsic operator techniques (using only products and ranks of tensor operators) is first evidenced by condensed proofs of already known $\bigtriangledown$-triangle sum rules of su(2)/su$_q$(2). {\em A new compact} su$_q$(2)-{\em expression} is found, using a $q$-series $Φ$, with $Φ(n)_{| q=1}=1$. This success comes from an ultimate identification process over monomials like $(c_0)^p$. For osp(1$|$2), analogous principles of calculation are transposed, involving a second parameter $d_0$. Ultimate identification process then must be done over binomials like ${(c_{0}+{d_{0}}^{2})}^{Ω-m} ({d_{0}}^{2})^{m}$. {\em Unknown} polynomials ${\cal P}$ are introduced as well as their expansion coefficients, $x$, over the binomials. It is clearly shown that a hypothetical super-triangle sum rule requires super-triangles $\bigtriangleup^{S}$, instead of $\bigtriangledown$ for su(2)/su$_q$(2). Coefficients $x$ are integers ({\em conjecture 1}). Massive unknown advances are done for intermediate steps of calculation. Among other, are proved {\em two theorems} on tensor operators, "zero" by construction. However, the ultimate identification seems to lead to a dead end, due to analytical apparent complexities. Up today, except for a few of coefficients $x$, no general formula is really available. | |
| dc.description | 39 pages | |
| dc.identifier | https://arxiv.org/abs/0811.2175 | |
| dc.identifier | http://arxiv.org/abs/0811.2175 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/174069 | |
| dc.subject | Mathematical Physics | |
| dc.subject | Quantum Algebra | |
| dc.subject | PACS: 02.20.Sv; 02.20.Uw; 11.30.Pb | |
| dc.title | Concept of a veritable osp(1$|$2) super-triangle sum rule with 6-$j^S$ symbols from intrinsic operator techniques: an open problem | |
| dc.type | text |