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


    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook