Schwinger-Dyson equation for non-Lagrangian field theory

A method is proposed of constructing quantum correlators for a general gaugesystem whose classical equations of motion do not necessarily follow from theleast action principle. The idea of the method is in assigning a certain BRSToperator $\hat\Omega$ to any classical equations of motion, Lagrangian or not.The generating functional of Green's functions is defined by the equation$\hat\Omega Z (J) = 0$ that is reduced to the standard Schwinger-Dyson equationwhenever the classical field equations are Lagrangian. The correspondingprobability amplitude $\Psi$ of a field $\phi$ is defined by the same equation$\hat\Omega \Psi (\phi) = 0$ although in another representation. When theclassical dynamics are Lagrangian, the solution for $\Psi (\phi)$ is reduced tothe Feynman amplitude $e^{\frac{i}{\hbar}S}$, while in the non-Lagrangian casethis amplitude can be a more general distribution.Comment: 33 page