Manuscript X-A-conv@1 · X-A-conv.tex · section · c76fffa3

Switch and boundary terms exposed

Independent action variation and the plateau Noether identity › Switch and boundary terms exposed · lines 1773–1796

X-A-conv@1#eq:switchedNoether

Applying (eq:Noetherzero)–(eq:Noethertwo) to (eq:switchedaction) gives, modulo $κ^{3}$ ,

δ_{ξ} S_{g}^{[2]} = \int \partial_{μ} n_{0}^{μ} + κ [\int \partial_{μ} (g n_{1}^{μ}) - \int (\partial_{μ} g) n_{1}^{μ} + \int (1 - g) δ_{ξ}^{(1)} ℓ_{0}] + κ^{2} [\int \partial_{μ} (g n_{2}^{μ}) - \int (\partial_{μ} g) n_{2}^{μ}] .

This identity is the varied-action calculation, not an inference from an intertwiner.

Displayed formulas in this passage

X-A-conv@1#eq:switchedNoether · line 1777
$δ_{ξ} S_{g}^{[2]} = \int \partial_{μ} n_{0}^{μ} + κ [\int \partial_{μ} (g n_{1}^{μ}) - \int (\partial_{μ} g) n_{1}^{μ} + \int (1 - g) δ_{ξ}^{(1)} ℓ_{0}] + κ^{2} [\int \partial_{μ} (g n_{2}^{μ}) - \int (\partial_{μ} g) n_{2}^{μ}] .$