Introduction
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In many instances transport properties can be described in terms of a local relationship between forces and currents. Examples are Fourier’s law of heat conduction $\boldsymbol{j}_{\varepsilon}=-\kappa\nabla T$, Fick’s law of diffusion $\boldsymbol{j}_{c}=-D\nabla\mu$, or Ohm’s law of electrical conduction $\boldsymbol{j}_{c}=\sigma\boldsymbol{E}.$ Here the thermal conductivity $\kappa$, the diffusion coefficient $D$, or the electrical conductivity $\sigma$ establish a relationship between the value of the forces, such as a temperature gradient or electric field, and the corresponding current density at the same location. Such local relations break down when the electron propagation is almost ballistic. Important examples worked out in particular by Brian Pippard are the nonlocal current-field relations to describe the Meissner effect in clean superconductors or the anomalous skin effect in clean metals[@Pippard1947; @Pippard1955; @Waldram1970]. However, non-local transport relations are not limited to the ballistic transport regime. Another example for non-local transport occurs when hydrodynamic flow of charge or heat sets in. Indeed, hydrodynamic flow patterns are frequently identified by complex “non-local” flow lines. It is therefore necessary to find closed expressions for the nonlocal heat conductivity $\kappa_{\alpha\beta}\left(\mathbf{r}-\mathbf{r}',t-t'\right)$, electrical conductivity $\sigma_{\alpha\beta}\left(\mathbf{r}-\mathbf{r}',t-t'\right)$ or even non-local shear viscosities $\eta$$\left(\mathbf{r}-\mathbf{r}',t-t'\right)$ of many-body systems in the hydrodynamic regime. In this regime collisions between partices 