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Eugeniu Plamadeala edited untitled.tex
about 9 years ago
Commit id: cf7b47a684f25b7b0a6856a52988592213d83d20
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$$ P = \frac{1}{4\pi} \sum_I k_{F,I} \left(\partial_x \phi_I - \partial_x \phi_{N+I} \right) + \frac{1}{4\pi} \sum_I \left( (\partial_x \phi_I)^2 - (\partial_x \phi_{N+I})^2 \right) $$
Fermion density. Giamarchi claims (eq 2.55), for a non-chiral boson, $ \rho_R(x) + \rho_L(x) = \frac{-1}{\pi}\partial_x
\phi. \phi $. In addition $\phi_R = K\theta - \phi, \phi_L = K \theta + \phi$. His final action for the chiral bosons looks like (C.12 upon above field redefinition)
$$ -S_G = \frac{1}{4\pi K} \int d\tau dx \left[ i \partial_\tau \phi_R \partial_x \phi_R - i \partial_\tau \phi_L \partial_x \phi_L - ... \right]$$
It looks just like the perfect metal action, so I conclude that (dropping the factor of K):