# Relative signs between interaction terms

What is the interpretation / meaning of relative signs between interaction terms in a Lagrangian density? (If there is none, are they even physically reasonable?)

Example: Let $$\phi$$ be a scalar field, then I am referring to Lagrangian densities such as $$L=\frac{1}{2}\partial_{\mu}\phi \partial^{\mu}\phi\,+\,\frac{\lambda_3}{3!} \phi^3 \,-\,\frac{\lambda_4}{4!} \phi^4.$$ Note the relative signs between the cubic and quartic interactions!

Note: This article did unfortunately not help as it was not properly answered.

• $L=T-V$ where $T$ is the kinetic energy (filed derivative squared) and $V$ is the potential energy. In this case $V=-\,\frac{\lambda_3}{3!} \phi^3 \,+\,\frac{\lambda_4}{4!} \phi^4$. May 8 at 16:04
• I mean the relative sign between the potential terms (In the qusetion I stated: "relative sign between INTERACTION terms"!). Is there any interpretation and if not, why not? May 8 at 16:16
• You might plot the potential and survey the locations of its minimum in the 4 distinct logical possibilities involved. May 8 at 16:24