# Applicability of Cardy's “doubling trick” to the 2D Ising Model

In Section 11.2.2 of the book on Conformal Field Theory by di Francesco, Mathieu, and Senechal (page 417), the two point function on the Upper Half Plane is written as being equal to the four point function in the CFT on the full complex plane:

$$G_{s}(y_1, y_2, \rho) \equiv \langle \sigma(z_1, \bar{\sigma}_1)\sigma(z_2, \bar{z}_2)\rangle_{UHP} = \langle \sigma(z_1)\sigma(z_2)\sigma(z_1^*)\sigma(z_2^*)\rangle$$

Also, the spin operator has conformal dimension $h = 1/16$, but this is presumably $\sigma(z)$. How does equating a two point function to a four point function respect conformal weights? Is it just because $\sigma(z_1)$ has half the conformal weight that $\sigma(z_1, \bar{z}_1)$ does?