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Robert Klauber’s second order photon propagator

  1. Jun 6, 2016 #1
    1. The problem statement, all variables and given/known data

    I have a question regarding Klauber's Student Friendly Quantum Mechanics, about renormalization in chapters 13 and 15. I have included all relevant equations in the attached document.

    In equation 15-105 he obtains an expression for the PI_uv(k^2) term used when calculating the second order photon propagator correction, which has a divergent part, A(k,Lambda), and a convergent part, PI_c(k^2). However the "convergent" part actually diverges for the particular case k^2 = 0 (unless I am wrong in my calculations).

    The problem with that is that in equation 13.52 it had been stated that the second order photon propagator D_uv(k) can be expressed as the first order propagator multiplied by 1 - eo^2 *A'(k, Lambda) - e0^2*PI_c(k^2). Then two pages later, in 13.62 the external photon polarization vector is conveniently renormalized by multiplying it by sqrt(1 - A'(A,k)), without the PI_c(k^2) term. He argues that it makes sense to remove the PI_c(k^2) term since any real photon (incoming or outgoing) will have k^2 = 0 and PI(k^2) can be expressed as a power expansion on k^2.

    It is therefore implied that PI(k^2) evaluated at k^2 is 0, although the exact explanation is provided in the solutions book (problem 13.5) which of course I do not have. The thing is, PI_c(k^2) is clearly divergent at k^2 = 0 so I do not think that the divergence disappears by doing a power expansion. Maybe the answer is that we can simply make the assumption that the actual nth order PI(k^2) would have the divergence at k^2 = 0 removed, leading to a 0 value. Anyway, I would like somebody to help me with this.

    Thanks in advance.

    2. Relevant equations


    See attached file.

    3. The attempt at a solution
     

    Attached Files:

  2. jcsd
  3. Jun 11, 2016 #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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