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Lost: Imaginary term in weak lagrangian

  • Thread starter Inge_k
  • Start date
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1. Homework Statement

I'm working on the last section of the last chapter (11.9 The Higgs Mechanism) of Griffith's book on Elementary Particles. In Problem 11.25 I'm asked to derive the lagrangian that he gets juts after gauging [Eq. 11.131]. That's the one with a Goldstone boson and a strange imaginary term that he doesn't want there too.
So, he starts with a model lagrangian in which he uses phi = phi1 + i phi2 . Then he finds the deviations of the vacuum state eta = phi1 - mu/lamda and xi = phi2 and my problem is to write the lagrangian in terms of eta and xi

2. Homework Equations

So I have
phi1 = eta + mu/lambda
phi2 = xi
And I fill this in in the Langrangian I already had

3. The Attempt at a Solution

Everything works out fine, except that all imaginary terms cancel. In the original langrangian there are two from the covariant derivatives and two from the complex phi. Multiplied with each other they vanish to give -1, multiplied with the other factors they cancel each other out. The term that should be imaginary in the end does appear on my final result, but it's missing a factor -2i .

I've looked everywhere, but I have no idea where to get that from. I'm sorry I'm not very good with Tex so I included a few mathematica screenshots. I hope it's clear.
 

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