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Questions from Schwinger's particles, sources and fields

  1. Nov 13, 2014 #1

    MathematicalPhysicist

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    Gold Member

    My first question from his first volume.

    On page 254, he writes down the action expression:

    [tex](3-10.1)W=\int (dx)[K\phi+K^{\mu}\phi_{\mu}+\mathcal{L}][/tex]
    Where the lagrangian is:
    [tex] \mathcal{L}=-\phi^{\mu}\partial_{\mu} \phi +1/2 \phi^{\mu}\phi_{\mu} -1/2 m^2 \phi^2 [/tex]


    The consideration of infinitesimal, variable phase transformations of the sources:

    [tex](3-10.2)\delta K(x) = ieq \delta \varphi (x) K(x) \ \ \delta K^{\mu}(x) = ieq \delta \varphi (x) K^{\mu}(x)[/tex]

    and of the compensating field transformations:
    [tex] \delta \phi (x) = ieq \delta \varphi (x) \phi(x) \ \ \delta \phi ^{\mu} (x) = ieq \delta \varphi (x) \phi^{\mu} [/tex]

    gives directly (I don't see it how exactly, can someone show me?):
    [tex](3-10.4) \delta W = \int (dx) [\phi((x) ieq K(x) + ieq \phi^{\mu} K_{\mu} ] \delta \varphi (x)[/tex]

    I don't see how did he get (3-10.4), can someone elighten me.

    Shouldn't he also take varaition of the lagrangian?!
     
  2. jcsd
  3. Nov 18, 2014 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
     
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