OPE of fermionic field bosonization in string theory, in Polchinski 10.3.12

Question

In Polchinski's String Theory Vol. 2, equations 10.3.12 are

$$e^{iH(z)}e^{-iH(-z)}~=~\frac{1}{2z}+i\partial H(0)+2zT_B^H(0)+O(z^2)\tag{10.3.12a}$$

$$\psi(z)\bar\psi(-z)~=~\frac{1}{2z}+\psi\bar\psi(0)+2zT_B^\psi(0)+O(z^2)\tag{10.3.12b}$$

How are these two OPEs calculated, especially the second and third terms?

This post imported from StackExchange Physics at 2014-10-15 14:05 (UTC), posted by SE-user Han Yan

Comments

Please consider explaining the notation in the equations and adding minimal context to make it accessible to people without access to Polchinski. Also, do you know how such OPE are calculated in general contexts, e.g. generic CFTs?

This post imported from StackExchange Physics at 2014-10-15 14:05 (UTC), posted by SE-user ACuriousMind