deletions | additions       diff --git a/untitled.tex b/untitled.tex  index a1146db..1d854a7 100644  --- a/untitled.tex  +++ b/untitled.tex 
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We agree that $\rho_e = \rho_R + \rho_L = e \sum_I \left( \psi^\dagger_{R,I} \psi_{R,I} + \psi^\dagger_{L,I} \psi_{L,I} \right)$.  Then the continuity equation implies  $$ j_e(x) = \frac{e}{\pi} \sum_{I=1}^N \sum_{J=1}^{2N} \left[ V_{I,J} - V_{N+I,J} \right] \partial_x \phi_J(x) $$ which is off by a factor of 2 from Mike's 1.22.