Manuscript VI-B@1 · VI-B-v1.tex · remark · 33798723

Remark: Dependence on the coordinate prescription

Finite-time harmonic coordinates and descent · lines 816–827

Changing coordinate Cauchy data is not a transformation of the specified gauge group. If $w$ is replaced by $w + a$ with $□ a = 0$ , then

O_{f}^{[1]} - O_{f}^{[1]} = - \int f a^{μ} \partial_{μ} ϕ_{0} d^{4} x,

which need not vanish. Descent therefore does not imply independence of the relational prescription.

Displayed formulas in this passage

unlabeled · line 820
$O_{f}^{[1]} - O_{f}^{[1]} = - \int f a^{μ} \partial_{μ} ϕ_{0} d^{4} x,$