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This implies that total momentum of fermions is  $$ P = - \sum_I k_{F,I} ( \psi^\dagger_{R,I} \psi_{R,I} - \psi^\dagger_{L,I} \psi_{L,I} )  + \sum_I \psi^\dagger_{R,I} (\psi^\dagger_{R,I}  (i\partial_x) \psi_{R,I} + \psi^\dagger_{L,I} (i\partial_x) \psi_{L,I} )$$  Bosons (we have a factor of 2 difference in the $k_F$ term Mike, eq 1.22)  $$ P = \frac{1}{4\pi} \sum_I k_{F,I} \left(