Analytical complements to the parity-independent racah-wigner calculus for the superalgebra osp(1|2). Part I
Lionel Bréhamet · Il Nuovo Cimento B · 2006
Essential simplifications are successfully carried out for all the phase factors occurring in various sum rules, formulas or expressions of mathematical tools, related to osp(1|2) parity-independent features. Another bringing-in lies in the introduction of a supertriangle Δ S in terms of integral parts, and of a symmetrical contraction phase factor g. From sometimes unusual techniques, new results are derived: a cyclic form of an identity between 3-j S symbols, intrinsic form of the irreducibility for any tensor operator, a linear identity between some special 6-j S symbols, a set of non-trivial zeros of 6-j S symbols, and-for the first time-explicit general analytical formulas for the 6-j S symbols. These latter are compact and given as a series over an integral index z in terms of Δ S and integral parts. A comparative synoptic of su(2) and osp(1|2) various formulas is supplied. New useful algebraic tables of boundary 6-j S symbols and those with one argument equal to 1 are listed.