Renormalization group

temperature and pressure point where phase boundaries disappear

Renormalization is a collection of techniques in quantum field theory, statistical field theory, and the theory of self-similar geometric structures, that is used to treat infinities arising in calculated quantities by altering values of these quantities to compensate for effects of their self-interactions. But even if no infinities arose in loop diagrams in quantum field theory, it could be shown that it would be necessary to renormalize the mass and fields appearing in the original Lagrangian.

phenomenon in certain quantum systems in which the coupling constant becomes small at high energy scales

parameter describing the strength of a force

physics of critical points

method for using scale changes to understand physical theories such as quantum field theories

type of approximation to an underlying physical theory

parameter describing physics near critical points

In quantum field theory, the energy that a particle has as a result of changes that it causes in its environment defines its self-energy \Sigma. The self-energy represents the contribution to the particle's energy, or effective mass, due to interactions between the particle and its environment. In electrostatics, the energy required to assemble the charge distribution takes the form of self-energy by bringing in the constituent charges from infinity, where the electric force goes to zero. In a condensed matter context, self-energy is used to describe interaction induced renormalization of quas

function that encodes the dependence of a coupling parameter on the energy scale

equation

renormalization scheme using dimensional regularization in 4+ε dimensions, in which the 1/ε terms are subtracted

energy scale (10²⁸⁶ eV) at which the interaction strength of quantum electrodynamics becomes infinite when computed perturbatively

situation quantum field theories with massless particles, in which Feynman integrals diverge due to low-energy (long-distance) contributions, requiring a cutoff representing detector threshold

situation in which a Feynman integral diverges due to high-energy (short-distance) contributions, requiring regularization/renormalization or some ultraviolet completion

maximum or minimum value for physics concepts