 Transformed SLE driving function

Apply the Itô formula to the transformed Loewner driving function ${\tilde{\xi }}_t={\varphi }_t(\sqrt{\kappa }{W}_t)$. The conformal conjugacy derivative for the chordal Loewner equation cancels the Itô drift exactly when $\kappa =6$. Its quadratic variation is $\kappa {\int }_0^t{\varphi }_s^{\prime }({\xi }_s{)}^{2}ds$.