Generalised Complex Contour Integral
We shall define the Generalised Complex Contour Integral as: \[ \oint_X \Delta[\phi]D\phi \equiv i \int\int \delta[X]\left( \overline{\Delta}[\overline{\phi}]\det\left[\frac{\delta X}{\delta \phi}\right] + \Delta[\phi] \det\left[\frac{\delta X}{\delta \overline{\phi}}\right] \right) D\phi D\overline{\phi} \] The function \[ \Delta[\phi] \] is for \[ S_0 \] : \[ \Delta[\phi] = \frac{1}{2\pi i (\phi_1 - \phi_2)}\] For \[S_n\] where n>0 \[ \Delta[\phi] = \frac{1}{\int \varepsilon_{abc..}\phi^a(x) \partial_1 \phi^b(x) \partial_2 \phi^c(x)... dx^n}\]