{{Short description|Process to make sure wave functions can induce probability distributions}} {{Use American English|date=January 2019}} {{refimprove |date=June 2025}} In quantum field theory, '''wave function renormalization''' is a rescaling (or renormalization) of quantum fields to take into account the effects of interactions.<ref>{{cite book|url=https://books.google.com/books?id=cGa5Q9BeMNUC&dq=%22Wave+function+renormalization%22+-wikipedia&pg=PA115|pages=113–117|title=Introduction to the Functional Renormalization Group|first1=Peter |last1=Kopietz|first2=Lorenz |last2=Bartosch|first3=Florian |last3=Schütz |year=2010|isbn=9783642050930|publisher=Springer|access-date=June 9, 2025}}</ref><ref>{{cite book|pages=384–385|url=https://books.google.com/books?id=rB_wdTnfTmoC&dq=%22Wave+function+renormalization%22+-wikipedia&pg=PA385|title=An Introduction to Quantum Field Theory|first=George |last=Sterman|year=1993|isbn=9780521311328|publisher=Cambridge University Press |access-date=June 9, 2025}}</ref>
For a noninteracting or free field, the field operator creates or annihilates a single particle with probability 1. Once interactions are included, however, this probability is modified in general to ''Z'' <math>\neq</math> 1.<ref>{{cite book|url=https://books.google.com/books?id=yykTDAAAQBAJ&dq=%22Wave+function+renormalization%22+-wikipedia&pg=PA137|pages=137–138|title=A Modern Introduction to Quantum Field Theory|first=Michele |last=Maggiore|year= 2005|isbn=9780198520733|publisher=Oxford University Press |access-date=June 9, 2025}}</ref>
This appears when one calculates the propagator beyond leading order; e.g. for a scalar field,
:<math>\frac{i}{p^2 - m_0^2 + i \varepsilon} \rightarrow \frac{i Z}{p^2 - m^2 + i \varepsilon}</math>
(The shift of the mass from ''m''<sub>0</sub> to m constitutes the mass renormalization.)
One possible wave function renormalization, which happens to be scale independent, is to rescale the fields so that the Lehmann weight (''Z'' in the formula above) of their quanta is 1. For the purposes of studying renormalization group flows, if the coefficient of the kinetic term in the action at the scale Λ is ''Z'', then the field is rescaled by <math>\sqrt{Z}</math>. A scale dependent wave function renormalization for a field means that that field has an anomalous scaling dimension.
==See also== *Renormalization
==References== {{reflist}}
{{DEFAULTSORT:Wave Function Renormalization}} Category:Renormalization group
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