The renormalization group
17.1 The renormalization group in quantum field theory
Most quantum field theories are nonlinear with infinitely many degrees of freedom and, because they describe point particles, they are rife with infinities. But short-distance effects, probably the finite sizes of the fundamental constituents of matter, mitigate these infinities so that we can cope with them consistently without knowing what happens at very short distances and very high energies. This procedure is called renormalization.
For instance, in the theory described by the Lagrange density
we can cut off divergent integrals at some high ...