The renormalization group

It has been around fifty years since Kenneth Wilson’s work on the renormalization group. Nature Physics celebrates this anniversary with a collection of Comments on its development and applications.

Renormalization began as a tool to eliminate divergences in quantum electrodynamics, but it is now the basis of our understanding of physics at different energy scales. Here, I review its evolution with an eye towards physics beyond the Wilsonian paradigm.

Kenneth Wilson worked on the renormalization group during the Cold War, when communication between scientists in the Soviet Union and in the West was restricted. Nevertheless, Soviet physicists had a strong influence on Wilson’s work.

The correct microscopic theory of quantum gravity may be an interacting, scale-invariant, ‘asymptotically safe’ model. This Comment discusses the renormalization group’s role in defining asymptotic safety and understanding its consequences.

Supersymmetric quantum field theories have special properties that make them easier to study. This Comment discusses how the constraints that supersymmetry places on renormalization group flows have been used to study strongly coupled field theories.

The renormalization group is a key ingredient in methods of improving perturbative computations in particle physics. Here I briefly discuss its role in perturbative quantum chromodynamics and particularly the running of its coupling constant.

Historically, most renormalization group studies have been performed for equilibrium systems. Here, I give a personal reflection on the unexpected outcome of studying non-equilibrium flocking using renormalization methods.

The renormalization group evolved from ad hoc procedures to cope with divergences in perturbative calculations. This Comment summarizes efforts to develop a mathematically rigorous approach to renormalization group calculations.