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Abelian Higgs model and conserved vortex current

  1. Dec 5, 2011 #1
    Refer page-24 in http://arxiv.org/abs/1010.0443v3

    Eq-6.19 is supposed to be the Lagrangian of Abelian-Higgs models. Eg-6.19 is clearly a conserved current of U(1) symmetry. But I cant show how eq-6.21 is a conserved vortex current.

    Note: The last term in the Lagrangian is not the usual [itex]F_{\mu \nu} F^{\mu \nu}[/itex].
  2. jcsd
  3. Dec 6, 2011 #2
    I see it now. I missed the fact that it is a 2+1 dimensional model :blushing:

    If it helps anyone...

    In 2+1 dimensions, [itex] \epsilon^{\mu \nu \lambda} \partial_\nu A_\lambda [/itex] (cf. 6.21) is proportional to the dual field strength tensor:
    [tex]\hat{J}^\mu \propto \tilde{F}^\mu = \star F_{\nu \lambda} [/tex]

    So, [itex][/itex] [itex]\hat{J}^\mu[/itex]is conserved simply by the Bianchi identity (or the homogeneous Maxwell equation):
    [tex]\partial_\mu \tilde{F}^\mu = 0 [/tex]

    PS: In 2+1 dim, [itex]( \epsilon^{\mu \nu \lambda} \partial_\nu A_\lambda )^2 \propto F_{\mu \nu} F^{\mu \nu} [/itex] (last term in the lagrangian of eq-6.19)
    Last edited: Dec 6, 2011
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