Manuscript XIV-C@1 · XIV-C.tex · input · a34d13df

Input statement: Eleven branches, copied

J1: copied branches, line orders, and collision inventory › Definitions used by the branch display · lines 659–679

XIV-C@1#input:branches, XIV-C@1#eq:branches

The full lift (eq:O) is $\sum_{j = 1}^{11} B_{j}$ , with

B_{1} B_{3} B_{5} B_{7} B_{9} B_{11} = - \int_{f} E_{m}^{R} (V_{1, g} [γ] p), = - \int_{f} X^{μ} \partial_{μ} p, = \int_{f} E_{0}^{R} (U_{σ}_{ε} [γ] X^{μ}) \partial_{μ} ϕ, = \frac{1}{2} \int_{f} X^{μ} X^{ν} \partial_{μ} \partial_{ν} ϕ, = \int_{f} p_{1} [r_{D}; ϕ], = \int_{f} p_{1} [r_{g}; ϕ] . B_{2} B_{4} B_{6} B_{8} B_{10} = - \int_{f} E_{m}^{R} (V_{2, g} [γ, 0] ϕ), = \int_{f} X^{ν} \partial_{ν} X^{μ} \partial_{μ} ϕ, = \int_{f} E_{0}^{R} (\partial_{α} (σ_{ε} a_{2}^{α μ} [γ])) \partial_{μ} ϕ, = - \int_{f} X_{1}^{μ} [r_{D}] \partial_{μ} ϕ, = - \int_{f} X_{1}^{μ} [r_{g}] \partial_{μ} ϕ,

The signs, affine slot identity, and inclusion of the scalar-sourced slot once are inherited from XIII-C XIIIC.

Displayed formulas in this passage

XIV-C@1#eq:branches · line 662
$B_{1} B_{3} B_{5} B_{7} B_{9} B_{11} = - \int_{f} E_{m}^{R} (V_{1, g} [γ] p), = - \int_{f} X^{μ} \partial_{μ} p, = \int_{f} E_{0}^{R} (U_{σ}_{ε} [γ] X^{μ}) \partial_{μ} ϕ, = \frac{1}{2} \int_{f} X^{μ} X^{ν} \partial_{μ} \partial_{ν} ϕ, = \int_{f} p_{1} [r_{D}; ϕ], = \int_{f} p_{1} [r_{g}; ϕ] . B_{2} B_{4} B_{6} B_{8} B_{10} = - \int_{f} E_{m}^{R} (V_{2, g} [γ, 0] ϕ), = \int_{f} X^{ν} \partial_{ν} X^{μ} \partial_{μ} ϕ, = \int_{f} E_{0}^{R} (\partial_{α} (σ_{ε} a_{2}^{α μ} [γ])) \partial_{μ} ϕ, = - \int_{f} X_{1}^{μ} [r_{D}] \partial_{μ} ϕ, = - \int_{f} X_{1}^{μ} [r_{g}] \partial_{μ} ϕ,$