What's the classical picture of phi^4 scalar field theory?

  • #1
I know that the classical picture of QED is Coulomb interaction, magnetic interaction etc. But what does the classical phi^4 theory look like? In particular, do particles attract or repel each other in this theory?

P.S. I'm surprised that my field theory books never discuss this. (At least in Peskin & Schroder's introductory chapter on scalar field theory.)
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  • #2
have you tried work it out for yourself?
  • #3
My intuition is that particles will repel each other to separate apart, because clumping together and forming large amplitudes is energetically unfavorable due to the phi^4 potential which grows faster than phi^2. Is this correct? I'll try to do some math when I have time.
  • #4
For [tex] \phi\phi \rightarrow \phi\phi [/tex] scattering, I think the scattering amplitude translates into a delta potential between the two mesons.

Whether the interaction is attractive or repulsive will depend on the sign of the delta potential which then depends on the coefficient of [tex] \phi^4 [/tex] in the Lagrangian.

I'm pretty sure that I saw this somewhere in a (non-advanced) field theory text. But correct me if what I said was wrong.

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