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Line vortex(strings)

  1. Jan 21, 2014 #1

    ChrisVer

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    Gold Member

    I am just trying to understand a little bit the concept behind this, but I feel lost.

    If we have the lagrangian:
    [itex]L= (D_{μ}Φ)(D^{μ}Φ^{*}) - \frac{1}{4} F_{μν}F^{μν}+ V(|Φ|^{2}) [/itex]
    with V being the Higg's Potential we can try to put as a solution of the dynamic system the relation:
    [itex]Φ(x)= ρ(r) e^{iθn2π} [/itex]
    This solution causes "problems" in the vacuum, because each winding of Φ stores up some energy.

    One question I have about it, is why is this the case? I understand that in the covariant derivatives, terms of [itex]∇_{θ}[/itex] will give additional energy proportional to the winding number n. But isn't the Φ field U(1) invariant? So I can make U(1) transformations which will cancel out the exponential factor giving me the Goldstone boson dof as longitudial dof of the gauge bosons?

    Also, any good book from which I can look up for Domain walls, these cosmic strings and GUT monoples would be appreciated :)

    Thanks
     
  2. jcsd
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