New information and entropic inequalities for Clebsch-Gordan coefficients
V.N. Chernega, O.V. Manko, V.I. Manko, and Z. Seilov
TL;DR
This paper derives new inequalities for SU(2) Clebsch-Gordan coefficients using Shannon and Tsallis entropies, linking them to probability distributions and special functions like Hahn polynomials.
Contribution
It introduces novel entropy-based inequalities for Clebsch-Gordan coefficients and related Wigner symbols, expanding the mathematical understanding of these quantum group representations.
Findings
New inequalities for Clebsch-Gordan coefficients and Wigner 3-j symbols
Connections established between entropic measures and special functions
Results applicable to quantum systems and mathematical physics
Abstract
The Clebsch-Gordan coefficients of the group SU(2) are shown to satisfy new inequalities. They are obtained using the properties of Shannon and Tsallis entropies. The inequalities associated with the Wigner 3-j symbols are obtained using the relation of Clebsch-Gordan coefficients with probability distributions interpreted either as distributions for composite systems or distributions for noncomposite systems. The new inequalities were found for Hahn polynomials and hypergeometric functions
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