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Renormalization is a collection of techniques in quantum field theory, statistical field theory, and the theory of self-similar geometric structures, that are 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 ...
e. 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 particle physics, it reflects the changes in the underlying force laws (codified in a quantum field theory) as the energy scale at which physical ...
In mean field theory, the mean field appearing in the single-site problem is a time-independent scalar or vector quantity. However, this isn't always the case: in a variant of mean field theory called dynamical mean field theory (DMFT), the mean field becomes a time-dependent quantity.
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 involves the beta function of the theory and the anomalous dimensions. As an example, for a quantum field theory with one massless scalar ...
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 within a class may differ dramatically at finite scales, their behavior will become increasingly similar as the limit scale is ...
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 dealing with strongly interacting systems. The method combines functional methods of quantum field theory with the ...
Critical dimension. In the renormalization group analysis of phase transitions in physics, a critical dimension is the dimensionality of space at which the character of the phase transition changes. Below the lower critical dimension there is no phase transition. Above the upper critical dimension the critical exponents of the theory become the ...
A different approach, called renormalized perturbation theory, is to use physically meaningful quantities from the very beginning. In the case of ϕ 4 theory, the field strength is first redefined: = /, where ϕ is the bare field, ϕ r is the renormalized field, and Z is a constant to be determined. The Lagrangian density becomes: