Action-derived scalar coefficients

Displayed formulas in this passage

• X-A-conv@1#eq:rhooneeq · line 1572

  $$\begin{array}{rl}{\square }_{\eta }{\rho }_{1,g}& =-V_{1,g}[h]{\rho }_0,\\ {\square }_{\eta }{\rho }_{2,g}& =-V_{1,g}[h]{\rho }_{1,g}-W_g[h,k]{\rho }_0.\end{array}$$

• X-A-conv@1#eq:rhotwoeq · line 1572

  $$\begin{array}{rl}{\square }_{\eta }{\rho }_{1,g}& =-V_{1,g}[h]{\rho }_0,\\ {\square }_{\eta }{\rho }_{2,g}& =-V_{1,g}[h]{\rho }_{1,g}-W_g[h,k]{\rho }_0.\end{array}$$

• X-A-conv@1#eq:rhoone · line 1581

  $$\begin{array}{rl}{\rho }_{1,g}& =-{\mathsf{E}}_0{V}_{1,g}[h]{\rho }_0,\\ {\rho }_{2,g}& ={\mathsf{E}}_0{V}_{1,g}[h]{\mathsf{E}}_0{V}_{1,g}[h]{\rho }_0-{\mathsf{E}}_0{W}_g[h,k]{\rho }_0.\end{array}$$

• X-A-conv@1#eq:rhotwo · line 1581

  $$\begin{array}{rl}{\rho }_{1,g}& =-{\mathsf{E}}_0{V}_{1,g}[h]{\rho }_0,\\ {\rho }_{2,g}& ={\mathsf{E}}_0{V}_{1,g}[h]{\mathsf{E}}_0{V}_{1,g}[h]{\rho }_0-{\mathsf{E}}_0{W}_g[h,k]{\rho }_0.\end{array}$$

• X-A-conv@1#eq:evalzero · line 1595

  $$\begin{array}{rl}{{\Phi }_g}^{[0]}& ={\rho }_0,\\ {{\Phi }_g}^{[1]}& ={\rho }_{1,g}-X_w{\rho }_0,\\ {{\Phi }_g}^{[2]}& ={\rho }_{2,g}-X_w{\rho }_{1,g}+\mathcal{J}(w){\rho }_0-X_v{\rho }_0.\end{array}$$

• X-A-conv@1#eq:evalone · line 1595

  $$\begin{array}{rl}{{\Phi }_g}^{[0]}& ={\rho }_0,\\ {{\Phi }_g}^{[1]}& ={\rho }_{1,g}-X_w{\rho }_0,\\ {{\Phi }_g}^{[2]}& ={\rho }_{2,g}-X_w{\rho }_{1,g}+\mathcal{J}(w){\rho }_0-X_v{\rho }_0.\end{array}$$

• X-A-conv@1#eq:evaltwo · line 1595

  $$\begin{array}{rl}{{\Phi }_g}^{[0]}& ={\rho }_0,\\ {{\Phi }_g}^{[1]}& ={\rho }_{1,g}-X_w{\rho }_0,\\ {{\Phi }_g}^{[2]}& ={\rho }_{2,g}-X_w{\rho }_{1,g}+\mathcal{J}(w){\rho }_0-X_v{\rho }_0.\end{array}$$

• unlabeled · line 1565

  $${\rho }_g={\rho }_0+\kappa {\rho }_{1,g}+{\kappa }^2{\rho }_{2,g}(\mathrm{mod}{\kappa }^3)$$