A W \right\}_{k K} 
\left\{ W ^{\dagger} A (UX) \right\}_{K k} 
\nonumber \\
&+& 
\sum_{n} \sum_{k} \sum_{K} \sum_{m \neq k} 
\biggl[
\frac{ (ix) }{ ( \Delta_{K} - h_{k} )^2 ( h_{m}  - h_{k} ) } 
e^{- i ( h_{k} - h_{n} ) x} 
\nonumber \\
&-& 
\frac{ (ix) }{ ( \Delta_{K} - h_{k} )^2 ( \Delta_{K} - h_{m} ) } 
e^{- i ( \Delta_{K} - h_{n} ) x} 
+
\frac{ ( h_{k} + 2 h_{m} - 3 \Delta_{K} ) }{ ( \Delta_{K} - h_{k} )^3 ( \Delta_{K} - h_{m} )^2 } 
e^{- i ( \Delta_{K} - h_{n} ) x} 
\nonumber \\
&+& 
\frac{ 1 }{ ( \Delta_{K} - h_{m} )^2 ( h_{m}  - h_{k} )^2 } 
e^{- i ( h_{m} - h_{n} ) x}
- 
\frac{ \left( \Delta_{K} + 2 h_{m} - 3 h_{k} \right) }{ ( \Delta_{K} - h_{k} )^3 ( h_{m}  - h_{k} )^2 } 
e^{- i ( h_{k} - h_{n} ) x} 
\biggr]
\nonumber \\ 
&\times&
(UX)_{\alpha k} (UX)^*_{\beta k} 
(UX)^*_{\alpha n} (UX)_{\beta n} 
\nonumber \\ 
&\times&
\left\{ (UX)^{\dagger} A W \right\}_{k K} 
\left\{ W ^{\dagger} A (UX) \right\}_{K m} 
\left\{ (UX)^{\dagger} A W \right\}_{m K} 
\left\{ W ^{\dagger} A (UX) \right\}_{K k} 
\nonumber \\
&+& 
\sum_{n} \sum_{k} \sum_{K \neq L} 
\biggl[
- \frac{x^2}{2} 
\frac{ 1 }{ ( \Delta_{K} - h_{k} ) ( \Delta_{L} - h_{k} ) } 
e^{- i ( h_{k} - h_{n} ) x} 
- (ix) 
\frac{ \left( \Delta_{K} + \Delta_{L} - 2 h_{k} \right) }{ ( \Delta_{K} - h_{k} )^2 ( \Delta_{L} - h_{k} )^2 } 
e^{- i ( h_{k} - h_{n} ) x} 
\nonumber \\
&-& 
\frac{ 1 }{ ( \Delta_{K} - h_{k} )^3 ( \Delta_{L} - \Delta_{K} ) } 
e^{- i ( \Delta_{K} - h_{n} ) x} 
+ \frac{ 1 }{ ( \Delta_{L} - h_{k} )^3 ( \Delta_{L} - \Delta_{K} ) } 
e^{- i ( \Delta_{L} - h_{n} ) x} 
\nonumber \\
&+& 
\frac{ 1 }{ ( \Delta_{K} - h_{k} )^3 ( \Delta_{L} - h_{k} )^3 } 
\biggl\{
\Delta_{L}^2 + \Delta_{L} \Delta_{K} + \Delta_{K}^2 - 3 h_{k} ( \Delta_{L} + \Delta_{K} ) + 3 h_{k}^2  
\biggr\}
e^{- i ( h_{k} - h_{n} ) x} 
\biggr]
\nonumber \\ 
&\times&
(UX)_{\alpha k} (UX)^*_{\beta k} 
(UX)^*_{\alpha n} (UX)_{\beta n} 
\nonumber \\ 
&\times&
\left\{ (UX)^{\dagger} A W \right\}_{k K} 
\left\{ W ^{\dagger} A (UX) \right\}_{K k} 
\left\{ (UX)^{\dagger} A W \right\}_{k L} 
\lef