Generalised Complex Contour Integral

We shall define the Generalised Complex Contour Integral as:

∮XΔ[ϕ]Dϕ≡i∫∫δ[X](Δ―[ϕ―]det[δXδϕ]+Δ[ϕ]det[δXδϕ―])DϕDϕ―

The function Δ[ϕ]  is for S0 :


Δ[ϕ]=12πi(ϕ1−ϕ2)


For Sn where n>0


Δ[ϕ]=1∫εabc..ϕa(x)∂1ϕb(x)∂2ϕc(x)...dxn


 


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