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Eugeniu Plamadeala edited untitled.tex
about 9 years ago
Commit id: 712e84bd6749f3eafc2198c1396ee4b68199baab
deletions | additions
diff --git a/untitled.tex b/untitled.tex
index 9fbda4d..2d7b209 100644
--- a/untitled.tex
+++ b/untitled.tex
...
$$ -S_G = \frac{1}{4\pi K} \int d\tau dx \left[ i \partial_\tau \phi_R \partial_x \phi_R - i \partial_\tau \phi_L \partial_x \phi_L - ... \right]$$
It looks just like the perfect metal action, but he has (eq 2.22) $\psi_R \propto e^{i k_F x} e^{i \phi_R}, \psi_L \propto e^{-i k_F x} e^{i \phi_L}$. That means our chiral fields are off by a minus sign:
$$ \phi_I
\equiv \phi^R_I = - \phi_R^{(G))} $$
$$ \phi_{N+I}
\equiv \phi^L_I = - \phi_L^{(G))} $$
so finally I conclude that: