  Given a semisimple reductive group $G$ and a smooth projective curve $X$ over
an algebraically closed field $k$ of arbitrary characteristic, let
$\text{Bun}_G$ denote the moduli space of principal $G$-bundles over $X$. For a
bundle $P\in\text{Bun}_G$ without infinitesimal symmetries, we provide a
description of all divided-power infinitesimal jet spaces,
$J_P^{n,PD}(\text{Bun}_G)$, of $\text{Bun}_G$ at $P$. The description is in
terms of differential forms on $X^n$ with logarithmic singularities along the
diagonals and with coefficients in $(\mathfrak{g}_P^*)^{\boxtimes n}$.
Furthermore, we show the pullback of these differential forms to the
Fulton-Macpherson compactification of the configuration space, $\hat{X}^n$, is
an isomorphism. Thus, we relate the two constructions of Beilinson-Drinfeld and
Beilinson-Ginzburg, and as a consequence, give a connection between
divided-power infinitesimal jet spaces of $\text{Bun}_G$ and the
$\mathcal{L}ie$ operad.
