- #1
ndung200790
- 519
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Please teach me this:
The linear sigma model L(Lagrangian)=[itex]\frac{1}{2}[/itex]([itex]\delta[/itex][itex]_{\mu}[/itex][itex]\Phi[/itex][itex]^{i}[/itex])[itex]^{2}[/itex] + [itex]\frac{1}{2}[/itex][itex]\mu[/itex][itex]^{2}[/itex]([itex]\Phi[/itex][itex]^{i}[/itex])[itex]^{2}[/itex] -
[itex]\frac{\lambda}{4}[/itex](([itex]\Phi[/itex][itex]^{i}[/itex])[itex]^{2}[/itex])[itex]^{2}[/itex].
The nonlinear sigma model:
L=f[itex]_{ij}[/itex]({[itex]\Phi[/itex][itex]^{i}[/itex]})[itex]\delta[/itex][itex]_{\mu}[/itex]
[itex]\Phi[/itex][itex]^{i}[/itex][itex]\delta[/itex][itex]^{\mu}[/itex][itex]\Phi[/itex][itex]{j}[/itex].
After put condition O(N) symmetry,we have Lagrangian(because after the putting f=constant):L=[itex]\frac{1}{2g^{2}}[/itex]/[itex]\delta[/itex][itex]_{\mu}[/itex]n/[itex]^{2}[/itex].
.Then the nonlinear model is a special case of the linear sigma model.So I do not understand why we call it the ''nonlinear'' model?
The linear sigma model L(Lagrangian)=[itex]\frac{1}{2}[/itex]([itex]\delta[/itex][itex]_{\mu}[/itex][itex]\Phi[/itex][itex]^{i}[/itex])[itex]^{2}[/itex] + [itex]\frac{1}{2}[/itex][itex]\mu[/itex][itex]^{2}[/itex]([itex]\Phi[/itex][itex]^{i}[/itex])[itex]^{2}[/itex] -
[itex]\frac{\lambda}{4}[/itex](([itex]\Phi[/itex][itex]^{i}[/itex])[itex]^{2}[/itex])[itex]^{2}[/itex].
The nonlinear sigma model:
L=f[itex]_{ij}[/itex]({[itex]\Phi[/itex][itex]^{i}[/itex]})[itex]\delta[/itex][itex]_{\mu}[/itex]
[itex]\Phi[/itex][itex]^{i}[/itex][itex]\delta[/itex][itex]^{\mu}[/itex][itex]\Phi[/itex][itex]{j}[/itex].
After put condition O(N) symmetry,we have Lagrangian(because after the putting f=constant):L=[itex]\frac{1}{2g^{2}}[/itex]/[itex]\delta[/itex][itex]_{\mu}[/itex]n/[itex]^{2}[/itex].
.Then the nonlinear model is a special case of the linear sigma model.So I do not understand why we call it the ''nonlinear'' model?