The Schwinger–Dyson equation on Peskin and Schroder reads (p.308):$$\!\!\!\!\!\!\!\!\left\langle\left(\frac{\delta}{\delta\phi(x)}\int d^4x'\mathcal L\right)\phi(x_1)...\phi(x_n)\right\rangle = \sum_{i=1}^n \left\langle\phi(x_1)...(i\delta(x-x_i))...\phi(x_n)\right\rangle \tag{9.88}$$
This equation tells us that the classical Euler-Lagrange equationsof the field $\phi$ are obeyed for all Green’s functions of $\phi$, up to contact termsarising from the nontrivial commutation relations of field operators.
In my QFT class we're told that those equations describe how fields and particles interact with each other. My question is how do we interpret this equation in a way that this interaction is clear? Can we tell how particles are excited from the associated quantum field from this equation, or can we tell which representation - particles or fields - is more fundamental?
