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{\bf Thermal current operator}. From Noether's theorem:  $$ T^{xt} = \frac{1}{4\pi} \left( \partial_t \phi_I K_{IJ} \partial_t \phi_J - 2 \partial_t \phi_I V_{IJ} \partial_x \phi_J \right) $$  {\bf Basis of almost conserved charges} charges}.  We will take the charge densities in each channel, and a piece of the total momentum:  \begin{align}  Q^R_I = \frac{e}{2\pi} \int dx \partial_x \phi_I \\