\(\renewcommand{\bar}{\overline} \renewcommand{\hat}{\widehat} \renewcommand{\tilde}{\widetilde} \newcommand{\bmit}[1]{\mathbf{\boldsymbol{#1}}} \newcommand{\vf}[1]{\mathbf{\boldsymbol{\vec{#1}}}} \renewcommand{\Hat}[1]{\mathbf{\boldsymbol{\hat{#1}}}} \newcommand{\vv}{\vf v} \newcommand{\grad}{\vf\nabla} \newcommand{\CC}{{\mathbb C}} \newcommand{\HH}{{\mathbb H}} \newcommand{\KK}{{\mathbb K}} \newcommand{\OO}{{\mathbb O}} \newcommand{\RR}{{\mathbb R}} \renewcommand{\SS}{{\mathbb S}} \newcommand{\ZZ}{{\mathbb Z}} \newcommand{\CP}{{\mathbb CP}} \newcommand{\HP}{{\mathbb HP}} \newcommand{\OP}{{\mathbb OP}} \newcommand{\RP}{{\mathbb RP}} \newcommand{\MM}{{\mathbf M}} \newcommand{\PP}{{\mathbf P}} \newcommand{\bH}{{\mathbf H}} \newcommand{\XX}{{\bmit X}} \newcommand{\YY}{{\bmit Y}} \newcommand{\AAA}{{\mathcal A}} \newcommand{\BBB}{{\mathcal B}} \newcommand{\III}{{\mathcal I}} \newcommand{\MMM}{{\mathcal M}} \newcommand{\XXX}{{\mathcal X}} \newcommand{\YYY}{{\mathcal Y}} \newcommand{\Lcal}{{\mathcal L}} \newcommand{\Pcal}{{\mathcal P}} \newcommand{\Qcal}{{\mathcal Q}} \newcommand{\Scal}{{\mathcal S}} \newcommand{\LL}{{\mathcal L}} \newcommand{\UU}{1} \renewcommand{\sl}{\mathfrak{sl}} \newcommand{\so}{\mathfrak{so}} \newcommand{\su}{\mathfrak{su}} \renewcommand{\sp}{\mathfrak{sp}} \newcommand{\spin}{\mathfrak{spin}} \newcommand{\uu}{\mathfrak{u}} \renewcommand{\aa}{\mathfrak{a}} \newcommand{\dd}{\mathfrak{d}} \newcommand{\ee}{\mathfrak{e}} \newcommand{\ff}{\mathfrak{f}} \renewcommand{\gg}{\mathfrak{g}} \newcommand{\hh}{\mathfrak{h}} \newcommand{\suL}{\su2_L} \newcommand{\suR}{\su2_R} \newcommand{\suc}{\su3_c} \newcommand{\Spin}{\mathrm{Spin}} \newcommand{\SO}{\mathrm{SO}} \newcommand{\SU}{\mathrm{SU}} \newcommand{\eA}{A} \newcommand{\eG}{G} \newcommand{\eS}{S} \newcommand{\eGS}{GS} \newcommand{\eD}{D} \newcommand{\eE}{E} \newcommand{\eF}{F} \newcommand{\eX}{X} \newcommand{\eY}{Y} \newcommand{\eZ}{Z} \newcommand{\up}{\uparrow} \newcommand{\dn}{\downarrow} \newcommand{\Ru}{R\up} \newcommand{\Rd}{R\dn} \newcommand{\Lu}{L\up} \newcommand{\Ld}{L\dn} \renewcommand{\Im}{{\mathrm{Im}}} \renewcommand{\Re}{{\mathrm{Re}}} \newcommand{\tr}{\mathrm{tr}} \newcommand{\Cl}{\mathrm{C}\ell} \newcommand{\bpsi}{{\boldsymbol\psi}} \newcommand{\mb}[1]{\mathbf{#1}} \newcommand{\HY}{\eta} \newcommand{\HYp}{\HY_{\mathrm{perp}}} \newcommand{\Sp}{\mathbf{S}} \newcommand{\eW}{R} \newcommand{\vp}{\varphi} \newcommand{\psid}{\vp(\psi)} \newcommand{\psib}{a(\psi)} \newcommand{\lt}{<} \newcommand{\gt}{>} \newcommand{\amp}{&} \)