# Relevant interaction terms based on dimension of coupling constants in quantum field theory

For a $$\phi^{3}$$ quantum field theory, the interaction term is $$\displaystyle{\frac{g}{3!}\phi^{3}}$$, where $$g$$ is the coupling constant.

The mass dimension of the coupling constant $$g$$ is $$1$$ in 4D, which means that $$\displaystyle{\frac{g}{E}}$$ is dimensionless.

Therefore, $$\displaystyle{\frac{g}{3!}\phi^{3}}$$ is a small pertubation at high energies $$E \gg g$$, but a large perturbation at low energies $$E \ll g$$.

Terms with this behavior are called relevant because they’re most relevant at low energies.

However, I do not understand why the interaction term is called relevant if we cannot use perturbation theory at low energies (where the term $$\displaystyle{\frac{g}{3!}\phi^{3}}$$ is a large pertubation). Is it because quantum field theory is only applicable in the relativistic limit, where $$E \gg g$$ and the perturbation is small?