Consider the complex degrees of freedom (q_{1}, q_{2} in mathbb{C}) forming a doublet (q=left(begin{array}{l}q_{1} q_{2}end{array} ight)),

Consider the complex degrees of freedom \(q_{1}, q_{2} \in \mathbb{C}\) forming a doublet \(q=\left(\begin{array}{l}q_{1} \\ q_{2}\end{array}\right)\), \(A=\sum_{i=1}^{3} a_{i} \sigma_{i} \in \mathbb{C}\), where \(\sigma_{i}\) are the Pauli matrices, and the Lagrangian

Show that \(L\) is invariant under \(S U(2)\).

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L = qq + det e q*Aq. - (14.82)