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How to do wick rotated surface int (srednicki ch75)

  1. Oct 16, 2011 #1

    I have the integral:

    [tex] \int\,\frac{d^4 l}{(2\pi)^4)} \frac{\partial}{\partial l^{\beta}} f_{\alpha}(l)[/tex]

    Now apparently this can be written (using a Wick rotation and converting to a surface integral) as:

    [tex] i \lim_{l\to\infty}\int\,\frac{\mathrm{d}S_{\beta}}{(2\pi)^4}\,f_{\alpha}(l) [/tex] where [tex]\mathrm{d}S_{\beta}=l^2 l_{\beta} d\Omega[/tex] is a surface-area element and [tex]d\Omega[/tex] is the differential solid angle in 4d.

    Can anyone see how exactly? (if context is needed this in (75.41) of Srednicki's QFT available free online)
  2. jcsd
  3. Oct 16, 2011 #2
    What I have already, well I understand the concept of a Wick rotation, but is this in the [itex] l^{0}[/itex] plane, such that we would write the Euclideanized variables as [itex] l^{0}=i \bar{l^{0}}[/itex], [itex]l^{j}=\bar{l}^{j}[/itex] and the Minkowski square [itex]-(q^{0})+(q^{1})^2+...[/itex] becomes the Euclidean +++.... square or something else?

    Then exactly how are we converting this integral to a surface integral? and how do we still have [itex] f_{\alpha}(l) [/itex] etc, not say [itex] f_{\alpha}(i l) [/itex] or something like that. Finally where does this limit outside come from?
  4. Oct 21, 2011 #3
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