Solution
= Solution
<Normal ordering> defines a composite field by subtracting all singular self-contractions before bringing its constituent points together. For example,
$$
{}:\!\partial X\partial X\!:(z)
=\lim_{w\to z}\left[
\partial X(z)\partial X(w)-
\langle\partial X(z)\partial X(w)\rangle\right].
$$
This makes $T$ and $\bar T$ well-defined local operators and is equivalent in oscillator language to placing creation operators to the left of annihilation operators.