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Schwinger-Dyson equation for non-Lagrangian field theory | | S.L.Lyakhovich
; A.A.Sharapov
; | | Date: |
11 Dec 2005 | | Journal: | JHEP 0602 (2006) 007 | | Abstract: | 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 $hatOmega$ to any classical equations of motion, Lagrangian or not. The generating functional of Green’s functions is defined by the equation $hatOmega Z (J) = 0$ 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 $hatOmega Psi (phi) = 0$ 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. | | Source: | arXiv, hep-th/0512119 | | Services: | Forum | Review | PDF | Favorites | |
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