Manuscript XVI-A@1 · XVI-A.tex · section · 8177be5d

Declared relations

Frozen declarations and notation › Declared relations · lines 219–257

XVI-A@1#eq:EH, XVI-A@1#eq:gf, XVI-A@1#eq:gaugefermion, XVI-A@1#eq:inverse, XVI-A@1#eq:preparedaction, XVI-A@1#eq:preparedsource, XVI-A@1#eq:sign

Back to manuscript

The following relations are retained exactly at the level of the supplied draft. No new coefficient, source formula, or wavefront estimate is inferred from them:

S_{EH} S_{gf} Ψ G_{gr}^{R} S_{grav, D} J_{D} = - \frac{2}{κ ^{2}} \int - q R, = \int D_{ν} (γ) D^{ν} (γ), = - i \int c ˉ_{μ} (2 D^{μ} γ - b^{μ}), = - P E_{0}^{R}, = S_{EH} + κ \int (σ_{ε} - 1) ℓ_{3}, = σ_{ε} J_{3} + D_{σ} .

The action–equation sign convention is

r = - u_{D} .

These formulas remain in the inherited integral notation. No unprovided measure, boundary condition, tensor contraction, or integration-by-parts prescription is silently reconstructed.

Displayed formulas in this passage

XVI-A@1#eq:EH · line 225
$S_{EH} S_{gf} Ψ G_{gr}^{R} S_{grav, D} J_{D} = - \frac{2}{κ ^{2}} \int - q R, = \int D_{ν} (γ) D^{ν} (γ), = - i \int c ˉ_{μ} (2 D^{μ} γ - b^{μ}), = - P E_{0}^{R}, = S_{EH} + κ \int (σ_{ε} - 1) ℓ_{3}, = σ_{ε} J_{3} + D_{σ} .$
XVI-A@1#eq:gf · line 225
$S_{EH} S_{gf} Ψ G_{gr}^{R} S_{grav, D} J_{D} = - \frac{2}{κ ^{2}} \int - q R, = \int D_{ν} (γ) D^{ν} (γ), = - i \int c ˉ_{μ} (2 D^{μ} γ - b^{μ}), = - P E_{0}^{R}, = S_{EH} + κ \int (σ_{ε} - 1) ℓ_{3}, = σ_{ε} J_{3} + D_{σ} .$
XVI-A@1#eq:gaugefermion · line 225
$S_{EH} S_{gf} Ψ G_{gr}^{R} S_{grav, D} J_{D} = - \frac{2}{κ ^{2}} \int - q R, = \int D_{ν} (γ) D^{ν} (γ), = - i \int c ˉ_{μ} (2 D^{μ} γ - b^{μ}), = - P E_{0}^{R}, = S_{EH} + κ \int (σ_{ε} - 1) ℓ_{3}, = σ_{ε} J_{3} + D_{σ} .$
XVI-A@1#eq:inverse · line 225
$S_{EH} S_{gf} Ψ G_{gr}^{R} S_{grav, D} J_{D} = - \frac{2}{κ ^{2}} \int - q R, = \int D_{ν} (γ) D^{ν} (γ), = - i \int c ˉ_{μ} (2 D^{μ} γ - b^{μ}), = - P E_{0}^{R}, = S_{EH} + κ \int (σ_{ε} - 1) ℓ_{3}, = σ_{ε} J_{3} + D_{σ} .$
XVI-A@1#eq:preparedaction · line 225
$S_{EH} S_{gf} Ψ G_{gr}^{R} S_{grav, D} J_{D} = - \frac{2}{κ ^{2}} \int - q R, = \int D_{ν} (γ) D^{ν} (γ), = - i \int c ˉ_{μ} (2 D^{μ} γ - b^{μ}), = - P E_{0}^{R}, = S_{EH} + κ \int (σ_{ε} - 1) ℓ_{3}, = σ_{ε} J_{3} + D_{σ} .$
XVI-A@1#eq:preparedsource · line 225
$S_{EH} S_{gf} Ψ G_{gr}^{R} S_{grav, D} J_{D} = - \frac{2}{κ ^{2}} \int - q R, = \int D_{ν} (γ) D^{ν} (γ), = - i \int c ˉ_{μ} (2 D^{μ} γ - b^{μ}), = - P E_{0}^{R}, = S_{EH} + κ \int (σ_{ε} - 1) ℓ_{3}, = σ_{ε} J_{3} + D_{σ} .$
XVI-A@1#eq:sign · line 249
$r = - u_{D} .$