This is a question for anyone who is familiar with Di Francesco's book on Conformal Field theory. In particular, on P.108 when he is deriving the general form of the 2-point Schwinger function in two dimensions. He writes that the most general form of the tensor is $$S_{\mu \nu \rho \sigma} = (x^2)^{-4} \left\{ A_1 g_{\mu \nu} g_{\rho \sigma} (x^2)^2 + A_2 (g_{\mu \rho}g_{\nu \sigma} + g_{\mu \sigma}g_{\nu \rho})(x^2)^2 + A_3(g_{\mu \nu}x_{\rho}x_{\sigma} + g_{\rho \sigma}x_{\mu}x_{\nu})x^2 + A_4 x_{\mu}x_{\nu}x_{\rho}x_{\sigma}\right\}$$ This I understand and have obtained this result myself. What I don't understand however, is why he has neglected the following term since it seems to satisfy all the constraints presented on P.108: $$S_{\mu \nu \rho\sigma} = A_5 (x^2)^{-3} (g_{\mu \sigma} x_{\rho}x_{\nu} + g_{\mu \rho}x_{\sigma}x_{\nu} + g_{\nu \sigma}x_{\rho}x_{\mu} + g_{\nu \rho}x_{\sigma}x_{\mu})$$ I wondered whether this could be reduced to terms already present in the form Di Francesco gave, but I quickly realized this to not be the case. So, if anyone is familiar with his book and would be willing to clarify this it would be great. I asked a professor at my university and he was not sure either why it has been neglected. He suggested that I impose the conservation law and then see that ##A_5## vanishes, but I tried this and it wasn't the case. This also would not explain why the tensor is not present in eqn (4.74) or in the first eqn I posted above.(adsbygoogle = window.adsbygoogle || []).push({});

Many thanks.

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# Derivation of Schwinger function in Di Francesco

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