An identity on SU(2) invariants

Kwee, Herry J.; Lebed, Richard F.

doi:10.1088/1751-8113/41/1/015206

J. Phys. A: Math. Theor.

2007

DOI: 10.1088/1751-8113/41/1/015206

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An identity on SU(2) invariants

Herry J. Kwee

Richard F. Lebed

Abstract: We prove an identity [Eq. (1) below] among SU(2) 6j and 9j symbols that generalizes the Biedenharn-Elliott sum rule. We prove the result using diagrammatic techniques (briefly reviewed here), and then provide an algebraic proof. This identity is useful for studying meson-baryon scattering in which an extra isoscalar meson is produced.

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Reduced form of statistical equilibrium equations and radiative transfer equations

Chichinin

2024

J. Phys. A: Math. Theor.

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An extension of the vector algebra for irreducible spherical tensor operators (ITOs) is proposed, which involves coupling two ITOs into a third one (V (kv)= T (kt)× U (ku)*), with the additional condition that one of the operators is a complex conjugate and therefore is not an ITO. The correctness condition is considered for this extension. The new coupling rule treats the density matrices ρ(Kl) and all tensors related to light polarization (J (Kr) or Τ (K)) equally.This approach has been applied to rewrite the fundamental statistical equilibrium equations and radiation transfer equations relevant to astrophysical polarimetry. The revised equations are more concise and eliminate the need for the nj symbols. Instead, they utilize vector and scalar products of ITOs. All rate coefficients in the equations consist of two independent factors, the reduced matrix element from dipole moments and the product (vector or scalar) of the tensors ρ(Kl) and J (Kr) (or Τ (K)).

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Reduced form of statistical equilibrium equations and radiative transfer equations

Chichinin

2024

J. Phys. A: Math. Theor.

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Pion electroproduction amplitude relations in the1/Ncexpansion

Cohen

Dakin

Lebed³

et al. 2009

Phys. Rev. D

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We derive expressions for pion electroproduction amplitudes in the 1/N c expansion of QCD, and obtain from them linear relations between the electromagnetic multipole amplitudes that hold at all energies. The leading-order relations in 1/N c compare favorably with available data (especially away from resonances), but the next-to-leading-order relations tend to provide only small or no improvement.

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An identity on SU(2) invariants

Cited by 2 publications

References 10 publications

Reduced form of statistical equilibrium equations and radiative transfer equations

Reduced form of statistical equilibrium equations and radiative transfer equations

Pion electroproduction amplitude relations in the1/Ncexpansion

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