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Variation of simple Lagrangian

  1. Jun 27, 2010 #1
    Hey, I'm doing some examples in QFT and I don't want to go too far with this one:

    Doing gauge symmetries, we first introduce the Unitary spacetime-dependent gauge transformation that gives us a gauge potential. With the new gauge added Lagrangian, I want to take its variation to confirm the equations of motion. Here's my question.

    When we take [tex]\frac{d}{d \phi} -m^2\phi^*\phi [/tex] for example...

    how do we handle the complex conjugate through our variation?
  2. jcsd
  3. Jun 28, 2010 #2


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    Usually you take it as an independent field, so you take the variation of the lagrangian with respect to phi (giving one equation) and with respect to phi* (giving another equation).

    If this construction troubles you, you can decompose phi into two real fields,
    [tex]\phi = \phi_1 + i \phi_2[/tex]
    and obtain the two equations by taking the variation with respect to phii (i = 1, 2).
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