In the canonical quantization approach for QFT, we deal with operators & their (anti)commutation relations. However, at the same time, we say that the field operators are the solutions of equation of motions such as Dirac, Klein-Gordon etc.
In the path integral approach we don't deal with commutation relations of field operators by definition. So where do the equation of motions (of which field operators are solutions) go?
How can we have a physical theory without equations of motion? And as an example, what would the analogue of the Klein-Gordon equation be in the path integral approach?
