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which is off by a factor of $4\pi$ from Mike's 1.22. (A $2\pi$ came from the commutator, and another 2 from the fact that one has to commute past 2 $\partial_x \phi$'s)  {\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}  We will take the charge densities in each channel, and a piece of the total momentum: