In quantum mechanics, most wave functions are normalized with \int |\phi|^2 dx^3 =1. But I did not see any field in the quantum field theory is normalized. I understand they maybe just plain waves and does not need to be normalized. But in some cases, if we do not expand the field as plain wave, how to normalize them? For instance, in the \lambda \phi 4 theory, the field \phi has the dimension of GeV. Should we use \int |\phi|^4 dx^4 =1 instead of \int |\phi|^2 dx^3 =1 or \int |\phi|^4 dx^3 =1?