# Derivation of Feynman Rules for a $\frac{1}{\phi}$ potential

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?

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