About integer-valued variants of the theta and 6j symbols - Archive ouverte HAL
Article Dans Une Revue Journal of Mathematical Physics Année : 2023

About integer-valued variants of the theta and 6j symbols

Résumé

These notes contain essentially a rewriting of several properties of two well-known quantities, the so-called theta symbol (or triangular symbol), which is rational, and the 6j symbol, which is usually irrational, in terms of two related integer-valued functions called gon and tet. Existence of these related integer-valued avatars, sharing most essential properties with their more popular partners, although a known fact, is often overlooked. The properties of gon and tet are easier to obtain, or to formulate, than those of the corresponding theta and 6j symbols, both in the classical and quantum situations. Their evaluation is also simpler (the paper displays a number of explicit formulae and evaluation procedures that may speed up some computer programs). These two integer-valued functions are unusual, in that their properties do not appear to be often discussed in the literature, but their features reflect those of related real-valued functions discussed in many places. Although our presentation is non-standard, the purpose of these notes is mostly pedagogical. Some of the properties that we shall discuss seem however to be new, in particular a relation with inverse Hilbert matrices. For its most part, the text does not require any familiarity with any specific scientific domain besides elementary arithmetics.

Dates et versions

hal-03815413 , version 1 (14-10-2022)

Identifiants

Citer

Robert Coquereaux. About integer-valued variants of the theta and 6j symbols. Journal of Mathematical Physics, 2023, 64 (3), pp.031703. ⟨10.1063/5.0131150⟩. ⟨hal-03815413⟩
21 Consultations
0 Téléchargements

Altmetric

Partager

More