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Mar 1, 2019 at 16:52 comment added physshyp if a and b depends on some coordintaes you have to take limint x-x'=0 so i think there is no problem.
Mar 1, 2019 at 16:11 comment added Weather Report There are several definitions of normal ordering and this causes some confusion. I think the one you used is not common in CFT. For example, the following formula for vertex operators is often cited $:e^{i\alpha_1\phi(z_1,\bar{z}_1)}::e^{i\alpha_2\phi(z_2,\bar{z}_2)}:=:e^{i\alpha_1\phi(z_1,\bar{z}_1)}e^{i\alpha_2\phi(z_2,\bar{z}_2)}:e^{-\alpha_1\alpha_2\langle\phi(z_1,\bar{z}_1)\phi(z_2,\bar{z}_2)\rangle}$. With your prescription correlator of any number of vertex correlators would be zero, independent of the neutrality condition.
Mar 1, 2019 at 15:49 history answered physshyp CC BY-SA 4.0