effective action functional in nLab

This entry is about the concept in quantum field theory. For the concept in group theory/representation theory see at effective group action; for disambiguation see effective action.

Contents

Idea

In the context of (perturbative) quantum field theory an effective action is an object obtained from a more fundamental (interaction) action functional by “averaging out” certain dependencies.

Details

• For the plain effective action see at S-matrix the section Effective action.

• More generally, for the relative effective action see at effective field theory the section Relative effective actions.

• quasiparticle

References

Introduction:

• Isabella Masina, Mariano Quiros: An introduction to effective potential methods in field theory [arXiv:2501.12713]

Discussion with an eye towards supersymmetric quantum field theory and Seiberg duality

• Flip Tanedo, section 2.1 of: Notes on Seibergology [pdf]

Review of effective actions in the background field formalism:

• Darren Trevor Grasso, section 3.1 of: Higher order contributions to the effective action of 𝒩=2\mathcal{N} = 2 and 44 supersymmetric Yang-Mills theories from heat kernel techniques in superspace Thesis (2007) (web)

In the context of the BV-BRST formalism:

• Kevin Costello. Renormalisation and the Batalin-Vilkovisky formalism (2007) [arXiv:0706.1533]

• Pavel Mnev: Discrete BF theory (2008). [arXiv:0809.1160]