Introduction to renormalization group
A renormalization group refers to a group that describes the transformation law of the renormalized Green's function (including matrix elements) in quantum field theory under the change of the renormalization mass scale. Renormalization is not the only way to separate the divergent part, because it is always necessary to introduce a running quality parameter μ during separation, which is equivalent to the selected quality scale is not unique. Because of this non-uniqueness, the renormalized Green's function must vary with μ. But the physical result does not change with μ. This invariance can be regarded as a kind of "group" invariance, and μ is the group parameter of the group. This group is called the renormalization group (in statistical physics and solid physics, the renormalization group is a semigroup).