Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    stevendaryl

    User Avatar
    Staff Emeritus
    Science Advisor

    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Solving phi-fourth theory using Fourier analysis
  1. Phi^4 theory (Replies: 3)

Loading...