The question is more mathematical in nature. If one had a potential $V(\phi) = \frac{\lambda}{\phi}$, where $\lambda$ is a constant, then how does one derive the Feynman rules for this scalar field's Lagrangian (assuming one is given the usual kinetic term)? Does one expand this as a Taylor series around some minimum and then find the rules?

  • $\begingroup$ Expanding about a minimum is generally a good idea, but in this case, where is your minimum? $\endgroup$ – gj255 Feb 12 '17 at 14:19
  • $\begingroup$ This looks quite non-perturbaative, since the stronges interaction will take place when the field $\phi$ is zero. $\endgroup$ – Mikael Fremling Feb 12 '17 at 14:20
  • $\begingroup$ related: physics.stackexchange.com/a/251515/84967 $\endgroup$ – AccidentalFourierTransform Feb 12 '17 at 14:23
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    $\begingroup$ The theory might be ill-defined in several ways... I assume you have considered Schwinger's formal wisecrack: $1/\phi=\int_0^\infty ds \exp (-s\phi) ~$? $\endgroup$ – Cosmas Zachos Feb 12 '17 at 14:23
  • $\begingroup$ @CosmasZachos I had actually not considered that, but how does that play a role here? $\endgroup$ – Cynthia's Light Feb 12 '17 at 14:47

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