equation as a Taylor series about , we get the entire set of Schwinger–Dyson equations. An example: φ4 To give an example, suppose for a real field φ. Then, The Schwinger–Dyson equation for this particular example is: Note that since is not well-defined because is a distribution in x1, x2 and x3, this equation needs to be regularized. In this example, the bare propagator D is the Green's function for and so, the Schwinger–Dyson set of equations goes as and etc. (Unless there is spontaneous symmetry breaking, the odd correlation functions vanish.) See also Functional renormalization group Dyson equation Path integral formulation References Further reading There are not many books that treat the Schwinger–Dyson equations. Here are three standard references: There are some review article about applications of the Schwinger–Dyson equations with applications to special field of physics. For applications to Quantum Chromodynamics there are Quantum field theory Differential equations Freeman Dyson