Source (quantum field theory, $J(x)$)

An external source is a prescribed field coupled to a dynamical field or operator in the action, for example $S_J=S_0+\int J_i(x){\varphi }_i(x)d^{d}x$. Functional derivatives of the generating functional with respect to $J$ insert the corresponding fields into correlation functions. The source is varied to generate these insertions, rather than integrated over as a dynamical degree of freedom. Transforming it in the appropriate representation maintains an invariant source coupling when deriving a Ward identity.