# Retarded vector potential and transverse current

While studying some topics on retarded potential, I came across the following statement, and I have some trouble understanding why this is true.

When we use the Coulumb gauge (instead of the Lorentz gauge), the equations for the scalar and vector potentials $$\phi_C$$ and $$\vec{A}_C$$ are no longer wave equations but can still be solved for the wave equation and Green function as,

$$\phi_C(\vec{r},t)=\int d^3r'\frac{\rho(\vec{r}',t)}{R} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \vec{A_C}(\vec{r},t)=\int d^3r\frac{\vec{j}_\bot(\vec{r}',t-R/c)}{R}$$

where $$R=|\vec{r}-\vec{r}|$$ and the transverse current is $$\vec{j}_\bot=\vec{j}-\nabla\frac{\partial}{\partial t}\phi$$.

It is evident that the scalar potential $$\phi$$ isn't retarded, and the vector potential $$\vec{A}$$ seems to be retarded since it depends of $$t-R/c$$ but it isn't retarded. This is due to the properties of $$\vec{j}_\bot$$.

Why isn't the vector potential retarded despite having a clear dependence on retarded time? Does the transverse current cancel that in some way, or how does it prevent it from being retarded?