Editing Effective action (section)

{{Quantum field theory|cTopic=Tools}}
{{short description|Quantum version of the classical action}}

In [[quantum field theory]], the '''quantum effective action''' is a modified expression for the [[classical physics|classical]] [[action (physics)|action]] taking into account quantum corrections while ensuring that the [[principle of least action]] applies, meaning that extremizing the effective action yields the [[equations of motion]] for the [[vacuum expectation value|vacuum expectation values]] of the quantum fields. The effective action also acts as a [[generating function|generating functional]] for one-particle irreducible [[Correlation function (quantum field theory)|correlation functions]]. The potential component of the effective action is called the '''effective potential''', with the expectation value of the true vacuum being the minimum of this potential rather than the classical potential, making it important for studying [[spontaneous symmetry breaking]].

It was first defined [[Perturbation theory|perturbatively]] by [[Jeffrey Goldstone]] and [[Steven Weinberg]] in 1962,<ref>{{cite journal|last1=Weinberg|first1=S.|authorlink1=Steven Weinberg|last2=Goldstone|first2=J.|authorlink2=Jeffrey Goldstone|date=August 1962|title=Broken Symmetries|url=https://link.aps.org/doi/10.1103/PhysRev.127.965|journal=Phys. Rev.|volume=127|issue=3|pages=965–970|doi=10.1103/PhysRev.127.965|bibcode=1962PhRv..127..965G |access-date=2021-09-06}}</ref> while the non-perturbative definition was introduced by [[Bryce DeWitt]] in 1963<ref>{{cite book|last1=DeWitt|first1=B.|author-link1=Bryce DeWitt|last2=DeWitt|first2=C.|date=1987|title=Relativité, groupes et topologie = Relativity, groups and topology : lectures delivered at Les Houches during the 1963 session of the Summer School of Theoretical Physics, University of Grenoble|location=|publisher=Gordon and Breach|isbn=0677100809}}</ref> and independently by [[Giovanni Jona-Lasinio]] in 1964.<ref>{{cite journal|last1=Jona-Lasinio|first1=G.|authorlink1=Giovanni Jona-Lasinio|date=31 August 1964|title=Relativistic Field Theories with Symmetry-Breaking Solutions|url=https://doi.org/10.1007/BF02750573|journal=Il Nuovo Cimento|volume=34|issue=6|pages=1790–1795|doi=10.1007/BF02750573|bibcode=1964NCim...34.1790J |s2cid=121276897 |access-date=2021-09-06}}</ref>

The article describes the effective action for a single [[scalar field theory|scalar field]], however, similar results exist for multiple scalar or [[fermionic field|fermionic]] fields.