# Category: Renormalization group

Effective field theory
In physics, an effective field theory is a type of approximation, or effective theory, for an underlying physical theory, such as a quantum field theory or a statistical mechanics model. An effective
Functional renormalization group
In theoretical physics, functional renormalization group (FRG) is an implementation of the renormalization group (RG) concept which is used in quantum and statistical field theory, especially when dea
Causal perturbation theory
Causal perturbation theory is a mathematically rigorous approach to renormalization theory, which makes it possible to put the theoretical setup of perturbative quantum field theory on a sound mathema
Minimal subtraction scheme
In quantum field theory, the minimal subtraction scheme, or MS scheme, is a particular renormalization scheme used to absorb the infinities that arise in perturbative calculations beyond leading order
Scaling limit
In mathematical physics and mathematics, the continuum limit or scaling limit of a lattice model refers to its behaviour in the limit as the lattice spacing goes to zero. It is often useful to use lat
Coupling constant
In physics, a coupling constant or gauge coupling parameter (or, more simply, a coupling), is a number that determines the strength of the force exerted in an interaction. Originally, the coupling con
Conformal anomaly
A conformal anomaly, scale anomaly, trace anomaly or Weyl anomaly is an anomaly, i.e. a quantum phenomenon that breaks the conformal symmetry of the classical theory. A classically conformal theory is
Ultraviolet fixed point
In a quantum field theory, one may calculate an effective or running coupling constant that defines the coupling of the theory measured at a given momentum scale. One example of such a coupling consta
Landau pole
In physics, the Landau pole (or the Moscow zero, or the Landau ghost) is the momentum (or energy) scale at which the coupling constant (interaction strength) of a quantum field theory becomes infinite
Multicritical point
Multicritical points are special points in the parameter space of thermodynamic or other systems with a continuous phase transition. At least two thermodynamic or other parameters must be adjusted to
Butcher group
In mathematics, the Butcher group, named after the New Zealand mathematician John C. Butcher by , is an infinite-dimensional Lie group first introduced in numerical analysis to study solutions of non-
Infrared fixed point
In physics, an infrared fixed point is a set of coupling constants, or other parameters, that evolve from initial values at very high energies (short distance) to fixed stable values, usually predicta
Self-energy
In quantum field theory, the energy that a particle has as a result of changes that it causes in its environment defines self-energy , and represents the contribution to the particle's energy, or effe
Beta function (physics)
In theoretical physics, specifically quantum field theory, a beta function, β(g), encodes the dependence of a coupling parameter, g, on the energy scale, μ, of a given physical process described by qu
Critical point (thermodynamics)
In thermodynamics, a critical point (or critical state) is the end point of a phase equilibrium curve. The most prominent example is the liquid–vapor critical point, the end point of the pressure–temp
On shell renormalization scheme
In quantum field theory, and especially in quantum electrodynamics, the interacting theory leads to infinite quantities that have to be absorbed in a renormalization procedure, in order to be able to
Universality class
In statistical mechanics, a universality class is a collection of mathematical models which share a single scale invariant limit under the process of renormalization group flow. While the models withi
Renormalization
Renormalization is a collection of techniques in quantum field theory, the statistical mechanics of fields, and the theory of self-similar geometric structures, that are used to treat infinities arisi
Quantum triviality
In a quantum field theory, charge screening can restrict the value of the observable "renormalized" charge of a classical theory. Ifthe only resulting value of the renormalized charge is zero, the the
Gaussian fixed point
A Gaussian fixed point is a fixed point of the renormalization group flow which is noninteracting in the sense that it is described by a free field theory. The word Gaussian comes from the fact that t
Critical exponent
Critical exponents describe the behavior of physical quantities near continuous phase transitions. It is believed, though not proven, that they are universal, i.e. they do not depend on the details of
Ultraviolet divergence
In physics, an ultraviolet divergence or UV divergence is a situation in which an integral, for example a Feynman diagram, diverges because of contributions of objects with unbounded energy, or, equiv
Loop integral
In quantum field theory and statistical mechanics, loop integrals are the integrals which appear when evaluating the Feynman diagrams with one or more loops by integrating over the internal momenta. T
Cutoff (physics)
In theoretical physics, cutoff (AE: cutoff, BE: cut-off) is an arbitrary maximal or minimal value of energy, momentum, or length, used in order that objects with larger or smaller values than these ph
Numerical renormalization group
The numerical renormalization group (NRG) is a technique devised by Kenneth Wilson to solve certain many-body problems where quantum impurity physics plays a key role.
Ultraviolet completion
In theoretical physics, ultraviolet completion, or UV completion, of a quantum field theory is the passing from a lower energy quantum field theory to a more general quantum field theory above a thres
Wave function renormalization
In quantum field theory wave function renormalization is a rescaling (or renormalization) of quantum fields to take into account the effects of interactions. For a noninteracting or free field the fie
Dangerously irrelevant operator
In statistical mechanics and quantum field theory, a dangerously irrelevant operator (or dangerous irrelevant operator) is an operator which is irrelevant at a renormalization group fixed point, yet a
Seiberg duality
In quantum field theory, Seiberg duality, conjectured by Nathan Seiberg in 1994, is an S-duality relating two different supersymmetric QCDs. The two theories are not identical, but they agree at low e
Dimensional transmutation
In particle physics, dimensional transmutation is a physical mechanism providing a linkage between a dimensionless parameter and a dimensionful parameter. In classical field theory, such as gauge theo
Callan–Symanzik equation
In physics, the Callan–Symanzik equation is a differential equation describing the evolution of the n-point correlation functions under variation of the energy scale at which the theory is defined and
Renormalization group
In theoretical physics, the term renormalization group (RG) refers to a formal apparatus that allows systematic investigation of the changes of a physical system as viewed at different scales. In part
Banks–Zaks fixed point
In quantum chromodynamics (and also N = 1 super quantum chromodynamics) with massless flavors, if the number of flavors, Nf, is sufficiently small (i.e. small enough to guarantee asymptotic freedom, d
Infrared divergence
In physics, an infrared divergence (also IR divergence or infrared catastrophe) is a situation in which an integral, for example a Feynman diagram, diverges because of contributions of objects with ve
Asymptotic freedom
In quantum field theory, asymptotic freedom is a property of some gauge theories that causes interactions between particles to become asymptotically weaker as the energy scale increases and the corres
Critical phenomena
In physics, critical phenomena is the collective name associated with thephysics of critical points. Most of them stem from the divergence of the correlation length, but also the dynamics slows down.
Pole mass
In quantum field theory, the pole mass of an elementary particle is the limiting value of the rest mass of a particle, as the energy scale of measurement increases.
Supersymmetry nonrenormalization theorems
In theoretical physics a nonrenormalization theorem is a limitation on how a certain quantity in the classical description of a quantum field theory may be modified by renormalization in the full quan
Asymptotic safety in quantum gravity
Asymptotic safety (sometimes also referred to as nonperturbative renormalizability) is a concept in quantum field theory which aims at finding a consistent and predictive quantum theory of the gravita
Physics applications of asymptotically safe gravity
The asymptotic safety approach to quantum gravity provides a nonperturbative notion of renormalization in order to find a consistent and predictive quantum field theory of the gravitational interactio
C-theorem
In quantum field theory the C-theorem states that there exists a positive real function, , depending on the coupling constants of the quantum field theory considered, , and on the energy scale, , whic