  We consider a set of elementary compactifications of $D+1$ to $D$ spacetime
dimensions on a circle: first for pure general relativity, then in the presence
of a scalar field, first free then with a non minimal coupling to the Ricci
scalar, and finally in the presence of gauge bosons. We compute the tree-level
amplitudes in order to compare some gravitational and non-gravitational
amplitudes. This allows us to recover the known constraints of the $U(1)$,
dilatonic and scalar Weak Gravity Conjectures in some cases, and to show the
interplay of the different interactions. We study the KK modes pair-production
in different dimensions. We also discuss the contribution to some of these
amplitudes of the non-minimal coupling in higher dimensions for scalar fields
to the Ricci scalar.
