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| \langle \Omega_{b_1} 0 \lambda_{b_1} | U_X | J_X m_X \rangle | | \langle \Omega_{b_1} 0 \lambda_{b_1} | U_X | J_X m_X \rangle |
| =\sum_{L_X} | | =\sum_{L_X} |
− | \left[ \sqrt{\frac{2J_X+1}{4\pi}} D_{m_X \lambda_{b_1}}^{J_X *}(\Omega_X,0) \right] | + | \left[ \sqrt{\frac{2J_X+1}{4\pi}} D_{m_X \lambda_{b_1}}^{J_X *}(\Omega_{b_1},0) \right] |
| \left[ \sqrt{\frac{2L_X+1}{2J_X+1}} | | \left[ \sqrt{\frac{2L_X+1}{2J_X+1}} |
| \left(\begin{array}{cc|c} | | \left(\begin{array}{cc|c} |
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| \langle \Omega_\omega 0 \lambda_\omega | U_{b_1} | 1 , m_{b_1}=\lambda_{b_1} \rangle | | \langle \Omega_\omega 0 \lambda_\omega | U_{b_1} | 1 , m_{b_1}=\lambda_{b_1} \rangle |
| =\sum_{L_{b_1}} | | =\sum_{L_{b_1}} |
− | \left[ \sqrt{\frac{2J_{b_1}+1}{4\pi}} D_{m_{b_1}=\lambda_{b_1} \lambda_\omega}^{1 *}(\Omega_{b_1},0) \right] | + | \left[ \sqrt{\frac{2J_{b_1}+1}{4\pi}} D_{m_{b_1} \lambda_\omega}^{1 *}(\Omega_\omega,0) \right] |
| \left[ \sqrt{\frac{2L_{b_1}+1}{2J_{b_1}+1}} | | \left[ \sqrt{\frac{2L_{b_1}+1}{2J_{b_1}+1}} |
| \left(\begin{array}{cc|c} | | \left(\begin{array}{cc|c} |
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| \langle \Omega_\rho 0 \lambda_\rho | U_\omega | 1 , m_\omega=\lambda_\omega \rangle | | \langle \Omega_\rho 0 \lambda_\rho | U_\omega | 1 , m_\omega=\lambda_\omega \rangle |
| =\sum_{L_\omega J_\rho} | | =\sum_{L_\omega J_\rho} |
− | \left[ \sqrt{\frac{2J_\omega+1}{4\pi}} D_{m_\omega=\lambda_\omega \lambda_\rho}^{1 *}(\Omega_\omega,0) \right] | + | \left[ \sqrt{\frac{2J_\omega+1}{4\pi}} D_{m_\omega \lambda_\rho}^{1 *}(\Omega_\rho,0) \right] |
| \left[ \sqrt{\frac{2L_\omega+1}{2J_\omega+1}} | | \left[ \sqrt{\frac{2L_\omega+1}{2J_\omega+1}} |
| \left(\begin{array}{cc|c} | | \left(\begin{array}{cc|c} |
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| \langle \Omega_{\pi^+} 0 \lambda_\rho | U_\rho | J_\rho , m_\rho=\lambda_\rho \rangle | | \langle \Omega_{\pi^+} 0 \lambda_\rho | U_\rho | J_\rho , m_\rho=\lambda_\rho \rangle |
| =\sum_{L_\rho} | | =\sum_{L_\rho} |
− | \left[ \sqrt{\frac{2J_\rho+1}{4\pi}} D_{m_\rho 0}^{J_\rho *}(\Omega_\rho,0) \right] | + | \left[ \sqrt{\frac{2J_\rho+1}{4\pi}} D_{m_\rho 0}^{J_\rho *}(\Omega_{\pi^+},0) \right] |
| \left[ \sqrt{\frac{2L_\rho+1}{2J_\rho+1}} | | \left[ \sqrt{\frac{2L_\rho+1}{2J_\rho+1}} |
| \left(\begin{array}{cc|c} | | \left(\begin{array}{cc|c} |
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| \right] | | \right] |
| f_{J_\rho\,0}^{J_\rho} | | f_{J_\rho\,0}^{J_\rho} |
− | =Y_{m_\rho}^{J_\rho}(\Omega_\rho) | + | =Y_{m_\rho}^{J_\rho}(\Omega_{\pi^+}) |
| f_{J_\rho\,0}^{J_\rho} | | f_{J_\rho\,0}^{J_\rho} |
| </math> | | </math> |
| | | |
− | * change subscripts on \Omega (e.g. X->b1)
| |
| * don't write m=lambda redundantly | | * don't write m=lambda redundantly |
| * be consistent about indexing of known spins | | * be consistent about indexing of known spins |