Vtyjkyuk

I wish to compute the variation of the energy momentum tensor under an infinitesimal conformal transformation, $w(z)=z+epsilon (z)$. I am following di Fransesco, who starts from the conformal ward identity;

$delta_epsilonlangle Xrangle =frac-12pi i oint_C dz epsilon(z)langle T(z)X rangle$

Where $X$ is a product of fields, and where $C$ encloses the location of each field.

From there di Francesco immediately jumps to;

$delta_epsilonT(w) =frac-12pi i oint_C dz epsilon(z) T(z)T(w)$

From here I can achieve the known result, but I don't understand how this jump is made. I can see that, taking $X=T(w)$, the first identity gives;

$delta_epsilonlangle T(w)rangle =frac-12pi i oint_C dz epsilon(z)langle T(z)T(w) rangle$

But I don't understand why the correlation function brackets can be dropped.

P.S. I'm not sure if this fits better here or over at physics SE, so feel free to move it if needed.