  We obtain a subgroup of the isometry group of $p$AdS (a $p$-adic version of
AdS alternative to the Bruhat-Tits tree). We propose a candidate for the scalar
bulk action and equation of motion on $p$AdS, and work out analytical
expressions of the Green's functions for a particular choice of parameter
together with an ansatz for general cases. The limiting behaviors of the
Green's function are also studied. With their help, the convergence of small
loops (whose radii are smaller than AdS length scale of $p$AdS) is analyzed.
