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About integer-valued variants of the theta and 6j symbols
- Source :
- J.Math.Phys., J.Math.Phys., 2023, 64 (3), pp.031703. ⟨10.1063/5.0131150⟩
- Publication Year :
- 2023
- Publisher :
- HAL CCSD, 2023.
-
Abstract
- 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. Some of the properties that we shall discuss seem however to be new, in particular several relations between the function gon and the inverse Hilbert matrices.<br />34 pages, 10 figures. Extended revised version: comments added, new references, new appendix, corrected typos
- Subjects :
- High Energy Physics - Theory
High Energy Physics - Theory (hep-th)
[PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th]
[PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph]
FOS: Mathematics
81R05, 22E99, 51M20
FOS: Physical sciences
Statistical and Nonlinear Physics
Mathematical Physics (math-ph)
Representation Theory (math.RT)
Mathematical Physics
Mathematics - Representation Theory
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Journal :
- J.Math.Phys., J.Math.Phys., 2023, 64 (3), pp.031703. ⟨10.1063/5.0131150⟩
- Accession number :
- edsair.doi.dedup.....b7cfd1b4c154e5da68c0fe3f273f68a7