 Logarithmic martingale for SLE4

For Schramm–Loewner evolution with $\kappa =4$ and $Z_t=g_t(z)-2W_t$, the Itô formula for the complex logarithm gives $d\log Z_t=-2Z_t^{-1}d{W}_t$ before swallowing. The drift cancels exactly at this parameter. Its real part is $\log |Z_t|$ and its imaginary part is the SLE4 angle martingale. The real-part quadratic variation is $4\int X_t^2/|Z_t{|}^{4}dt$, which also gives a direct non-swallowing argument.