I have a question about the notation in Silverman's Arithmetic of EC. On page 2, "Notice that the Galois group $G_{\overline{K}/K}$ acts on $\mathbb{A}^n$; for $\sigma\in G_{\overline{K}/K}$ and $P\in \mathbb{A}^n$, $$P^\sigma=(x_1^\sigma,\dots,x_n^\sigma)."$$
Does $x^\sigma=\sigma(x)$?