Let's take a look at the Feynman propagator for a massive scalar field:

$$D_F(x-y)=\int\frac{dp^3}{(2\pi)^3}\int\frac{dp^0}{2\pi}\frac{ie^{-i(x-y)}}{p^2-m^2}$$

We can use this as the Green's function for a function $u(x)$ with a corresponding $f(y)$:

$$u(x)=\int f(y)G(x-y)dy$$

My question is about the $u(x)$ and the $f(y)$. How are these related to the fields? ARE they the fields? I mean, can we insert, in this case, the scalar field $\phi(x)$?

Let's take a look at the Feynman propagator for a massive scalar field:

$$D_F(x-y)=\int\frac{dp^3}{(2\pi)^3}\int\frac{dp^0}{2\pi}\frac{ie^{-ip \cdot (x-y)}}{p^2-m^2}$$

We can use this as the Green's function for a function $u(x)$ with a corresponding $f(y)$:

$$u(x)=\int f(y)G(x-y)dy$$

My question is about the $u(x)$ and the $f(y)$. How are these related to the fields? ARE they the fields? I mean, can we insert, in this case, the scalar field $\phi(x)$?