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Solving phi-fourth theory using Fourier analysis

  1. Dec 30, 2015 #1
    The equation of motion of ##\phi^4## theory is ##(\partial^{2}+m^{2})\phi = -\frac{\lambda}{3!}\phi^{3}##.

    Why can't this equation be solved using Fourier analysis? Can't we simply write the equation in Fourier space and take it from there?
  2. jcsd
  3. Dec 30, 2015 #2


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    Well, the right-hand side of the equation is nonlinear, so performing a Fourier transform will produce a mess---a triple integral. You end up replacing a nonlinear differential equation by a nonlinear integral equation. That might be a good first step, but it doesn't solve the equation. You would have to resort to perturbation theory in any case.
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