The Schwinger–Dyson equations (SDEs) are a set of equations in quantum field theory that describe the behavior of Green's functions (correlation functions or propagators) of quantum fields. They are a crucial tool in the study of non-perturbative phenomena in quantum field theories and are derived from the fundamentals of functional integration and the principles of quantum mechanics.
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A Schwinger-Dyson equation follows from invariance of a path integral under a change of integration variable and relates correlation functions through the field equations and contact terms.