The “exact” or “functional” renormalization group equation describes the renormalization group flow of the effective average action Γ k. The ordinary effective action Γ 0 can be obtained by integrating the flow equation from an ultraviolet scale k= Λ down to k= 0. We give several examples of such calculations at one-loop, both in renormalizable and in effective field theories. We reproduce the four-point scattering amplitude in the case of a real scalar field theory with quartic potential and in the case of the pion chiral Lagrangian. In the case of gauge theories, we reproduce the vacuum polarization of QED and of Yang–Mills theory. We also compute the two-point functions for scalars and gravitons in the effective field theory of scalar fields minimally coupled to gravity. © 2016, The Author(s).

Computing the effective action with the functional renormalization group

Percacci, Roberto;
2016-01-01

Abstract

The “exact” or “functional” renormalization group equation describes the renormalization group flow of the effective average action Γ k. The ordinary effective action Γ 0 can be obtained by integrating the flow equation from an ultraviolet scale k= Λ down to k= 0. We give several examples of such calculations at one-loop, both in renormalizable and in effective field theories. We reproduce the four-point scattering amplitude in the case of a real scalar field theory with quartic potential and in the case of the pion chiral Lagrangian. In the case of gauge theories, we reproduce the vacuum polarization of QED and of Yang–Mills theory. We also compute the two-point functions for scalars and gravitons in the effective field theory of scalar fields minimally coupled to gravity. © 2016, The Author(s).
2016
76
4
1
24
226
10.1140/epjc/s10052-016-4063-3
https://arxiv.org/abs/1505.03119
http://inspirehep.net/record/1369330
http://cdsads.u-strasbg.fr/abs/2016EPJC...76..226C
Codello, A.; Percacci, Roberto; Rachwal, L.; Tonero, A.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/11894
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