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A question about symmetry in the phi^4 theory

  1. Jun 22, 2015 #1
    1. The problem statement, all variables and given/known data
    Why does the symmetry ##\phi\rightarrow-\phi## mean that an amplitude can be written as
    ##\alpha + \beta p^2 + \gamma p^4 + ...##
    without the odd terms in ##p##?
    2. Relevant equations
    I understand that, due to this symmetry, any diagram in ##\phi^4## has an even number of external legs, because otherwise the correlation function of the external fields is zero. So any diagram can be written in the form
    ##V(p^2)\left(\frac{i}{p^2-m^2}\right)^{n}##
    where ##n## is even and ##V(p^2)## is the expression for the amplitude without the external legs. Expanding ##V(p^2)## in ##p## will, of course, give only even powers of ##p##, as will the expansion of ##\left(\frac{i}{p^2-m^2}\right)^n##, but that is true also for ##n## odd, corresponding to an odd number of external legs. So where does this symmetry play a role here?

    3. The attempt at a solution
    Outlined in (2).
     
  2. jcsd
  3. Jun 27, 2015 #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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