Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2005-12-11
JHEP0602:007,2006
Physics
High Energy Physics
High Energy Physics - Theory
33 pages
Scientific paper
10.1088/1126-6708/2006/02/007
A method is proposed of constructing quantum correlators for a general gauge system whose classical equations of motion do not necessarily follow from the least action principle. The idea of the method is in assigning a certain BRST operator $\hat\Omega$ 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 equation whenever the classical field equations are Lagrangian. The corresponding probability amplitude $\Psi$ of a field $\phi$ is defined by the same equation $\hat\Omega \Psi (\phi) = 0$ although in another representation. When the classical dynamics are Lagrangian, the solution for $\Psi (\phi)$ is reduced to the Feynman amplitude $e^{\frac{i}{\hbar}S}$, while in the non-Lagrangian case this amplitude can be a more general distribution.
Lyakhovich Simon L.
Sharapov Alexey A.
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