= Logarithmic martingale for SLE4
{title2=$d\log Z_t=-2Z_t^{-1}dW_t$}
For <Schramm–Loewner evolution> with $\kappa=4$ and $Z_t=g_t(z)-2W_t$, the <Itô formula> for the <complex logarithm> gives $d\log Z_t=-2Z_t^{-1}dW_t$ 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.
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