I'm looking at the simplest example of an interacting theory, and this is the theory of a neutral scalar boson $\phi$ with $\lambda \phi^4$ interaction term. Can I ask: is there a physical interpretation of the `charge' through which this field interacts with itself? In particular, is \lambda a property of the field in something like the way that the electrical charge of the electron is both a property of it and a measure of the coupling strength? (I am unsure of this latter analogy, as in the electrical case the charge property is understood as the invariant of the U(1) symmetry of the free electron Lagrangian; but the symmetry here is $Z_2$, so not continuous -- hence we can't use Noether's theorem.) Any help much appreciated!