Computational electromagnetics: Difference between revisions
en>Martin Timm →Choice of methods: Deleted HFSS paragraph (adverising), section should be more general, and help with choice of methods |
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{{Unreferenced stub|auto=yes|date=December 2009}} | |||
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 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. This shows up when one calculates the [[propagator]] beyond [[leading-order|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. (It's trickier to define it for unstable particles). For the purposes of studying [[renormalization group flow]]s, 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 wavefunction renormalization for a field means that that field has an [[anomalous scaling dimension]]. | |||
==See also== | |||
*[[Renormalization]] | |||
{{DEFAULTSORT:Wave Function Renormalization}} | |||
[[Category:Quantum field theory]] | |||
[[Category:Renormalization group]] | |||
{{Quantum-stub}} | |||
Revision as of 06:57, 26 December 2013
Template:Unreferenced stub 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 field operator creates or annihilates a single particle with probability 1. Once interactions are included, however, this probability is modified in general to Z 1. This shows up when one calculates the propagator beyond leading order; e.g., for a scalar field,
(The shift of the mass from m0 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. (It's trickier to define it for unstable particles). 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 . A scale dependent wavefunction renormalization for a field means that that field has an anomalous scaling dimension.