quantum field theory In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles a ...

wave function renormalization is a rescaling (or

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 arising in calculated quantities by altering ...

) of quantum fields to take into account the effects of interactions. For a noninteracting or

free field In physics a free field is a field without interactions, which is described by the terms of motion and mass. Description In classical physics, a free field is a field whose equations of motion are given by linear partial differential equ ...

, the

field operator In physics, canonical quantization is a procedure for quantizing a classical theory, while attempting to preserve the formal structure, such as symmetries, of the classical theory, to the greatest extent possible. Historically, this was not qu ...

creates or annihilates a single particle with

probability Probability is the branch of mathematics concerning numerical descriptions of how likely an Event (probability theory), event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and ...

1. Once interactions are included, however, this probability is modified in general to ''Z''

\neq

1. This appears when one calculates the

propagator In quantum mechanics and quantum field theory, the propagator is a function that specifies the probability amplitude for a particle to travel from one place to another in a given period of time, or to travel with a certain energy and momentum. ...

beyond

leading order The leading-order terms (or corrections) within a mathematical equation, expression or model are the terms with the largest order of magnitude.J.K.Hunter, ''Asymptotic Analysis and Singular Perturbation Theory'', 2004. http://www.math.ucdavis.edu/~ ...

; e.g. for a scalar field, :

\frac \rightarrow \frac

(The shift of the mass from ''m''₀ to m constitutes the

mass renormalization In quantum field theory, the energy that a particle has as a result of changes that it causes in its environment defines self-energy \Sigma, and represents the contribution to the particle's energy, or effective mass, due to interactions between ...

.) One possible wave function renormalization, which happens to be scale independent, is to rescale the fields so that the

Lehmann weight Lehmann is a German surname. Geographical distribution As of 2014, 75.3% of all bearers of the surname ''Lehmann'' were residents of Germany, 6.6% of the United States, 6.3% of Switzerland, 3.2% of France, 1.7% of Australia and 1.3% of Poland. In ...

(''Z'' in the formula above) of their quanta is 1. For the purposes of studying

renormalization group flow 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 t ...

s, if the coefficient of the kinetic term in the action at the scale Λ is ''Z'', then the field is rescaled by

\sqrt

. A scale dependent wave function renormalization for a field means that that field has an

anomalous scaling dimension In theoretical physics, the scaling dimension, or simply dimension, of a local operator in a quantum field theory characterizes the rescaling properties of the operator under spacetime dilations x\to \lambda x. If the quantum field theory is sca ...

See also