computation more compact using v{b}

Doc/DevRef/Polarized.tex

@@ -182,24 +182,24 @@ implemented in functions
 
 With the abbreviations
 \begin{equation}
-  \alpha \coloneqq \evp_+ + \evp_-
-  \quad\text{and}\quad
-  \beta \coloneqq \evp_+ - \evp_-,
+  \alpha \coloneqq \evp_+ + \evp_-,\quad
+  \beta \coloneqq \evp_+ - \evp_-,  \quad\text{and}\quad
+  \v{b} \coloneqq \beta \eB,
 \end{equation}
 the wavenumber operator~\cref{Ehp1} is computed as
 \begin{equation}
-\opkappa = \frac{1}{2}  \left( \alpha + \beta \; \eB \Pauli  \right)
+\opkappa = \frac{1}{2}  \left( \alpha + \v{b} \Pauli  \right)
          = \frac{1}{2} \begin{pmatrix}
-              \alpha + \beta e_z & \beta \left( e_x - i e_y \right)\\
-              \beta \left( e_x + i e_y \right) & \alpha - \beta e_z
+              \alpha + b_z & b_x - i b_y\\
+              b_x + i b_y & \alpha - b_z
           \end{pmatrix}.
 \end{equation}
 The inverse~\cref{Ehpi} is computed as
 \begin{equation}
 \opkappa^{-1} = \frac{2}{\alpha^2 - \beta^2}
              = \begin{pmatrix}
-                 \alpha - \beta e_z & -\beta \left( e_x - i e_y \right)\\
-                 -\beta \left( e_x + i e_y \right) & \alpha + \beta e_z
+                 \alpha - b_z & -b_x + i b_y\\
+                 -b_x - i b_y & \alpha + b_z
             \end{pmatrix} \,.
 \end{equation}
 }