Manuscript X-E-ST@1 · X-E-ST.tex · section · 44614221

Matter variation and the complete Euler equation

E1: action, Palatini variation, and switched Noether identity › Matter variation and the complete Euler equation · lines 560–571

Set

T^{μν} [q, ϕ] = q^{μα} q^{ν β} \partial_{α} ϕ \partial_{β} ϕ - \frac{1}{2} q^{μν} (q^{α β} \partial_{α} ϕ \partial_{β} ϕ - m^{2} ϕ^{2}),

and write $T_{0} = T [η, ϕ]$ .

Displayed formulas in this passage

unlabeled · line 563
$T^{μν} [q, ϕ] = q^{μα} q^{ν β} \partial_{α} ϕ \partial_{β} ϕ - \frac{1}{2} q^{μν} (q^{α β} \partial_{α} ϕ \partial_{β} ϕ - m^{2} ϕ^{2}),$