A stationary composition law for Schwinger-Keldysh effective actions
- 1INFN — Sezione di Ferrara
Abstract
Let W𝒪[J] and W𝒞[J] denote the connected generating functionals of an open system and its closed system counterpart, and define the environment-induced contribution WIF[J] by the difference: WIF[J] ≡ W𝒪[J] − W𝒞[J]. The corresponding Legendre transforms, Γ𝒪, Γ𝒞, and ΓIF, do not obey an analogous additive relation but satisfy a stationary composition law given by: Γ O Φ = Stat Ψ Γ C Ψ + Γ IF Φ − Ψ Γ𝒪[Φ ]=undersetΨStat{Γ𝒞[Ψ ]+ΓIF[Φ −Ψ ]}
where Stat denotes evaluation at a solution of the stationarity condition with respect to Ψ. This variational composition applies to both local and nonlocal Schwinger-Keldysh effective actions in nonequilibrium quantum field theory. We illustrate its linear and nonlinear realizations through quadratic theories and general time independent effective actions, respectively.
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BibTeX
@article{comelli2026stationary,
title = {{A stationary composition law for Schwinger-Keldysh effective actions}},
author = {Denis Comelli},
journal = {Journal of High Energy Physics},
year = {2026},
month = nov,
doi = {10.1007/jhep11(2026)032},
url = {https://link.springer.com/article/10.1007/JHEP11(2026)032},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - A stationary composition law for Schwinger-Keldysh effective actions
AU - Denis Comelli
PY - 2026
DA - 2026/11/04
JO - Journal of High Energy Physics
DO - 10.1007/jhep11(2026)032
UR - https://link.springer.com/article/10.1007/JHEP11(2026)032
AB - Let W𝒪[J] and W𝒞[J] denote the connected generating functionals of an open system and its closed system counterpart, and define the environment-induced contribution WIF[J] by the difference: WIF[J] ≡ W𝒪[J] − W𝒞[J]. The corresponding Legendre transforms, Γ𝒪, Γ𝒞, and ΓIF, do not obey an analogous additive relation but satisfy a stationary composition law given by: Γ O Φ = Stat Ψ Γ C Ψ + Γ IF Φ − Ψ Γ_𝒪[Φ ]=undersetΨStat{Γ_𝒞[Ψ ]+Γ_IF[Φ −Ψ ]} where Stat denotes evaluation at a solution of the stationarity condition with respect to Ψ. This variational composition applies to both local and nonlocal Schwinger-Keldysh effective actions in nonequilibrium quantum field theory. We illustrate its linear and nonlinear realizations through quadratic theories and general time independent effective actions, respectively.
SN - 1029-8479
ER -