AI 中文总结
该研究针对非平衡量子场论，提出开放系统与封闭系统对应施温格-凯尔迪什有效作用量的定态合成律，阐释其线性与非线性实现形式，为相关领域提供关键变分关系。
AI 中文摘要
令$W_{\cal O}[J]$和$W_{\cal C}[J]$分别表示开放系统及其对应封闭系统的连通生成泛函，定义环境诱导贡献$W_{\rm IF}[J]$为二者之差：$W_{\rm IF}[J]\equiv W_{\cal O}[J]-W_{\cal C}[J]$。对应的勒让德变换$\Gamma_{\cal O}$、$\Gamma_{\cal C}$和$\Gamma_{\rm IF}$不满足类似的加和关系，而是满足如下定态合成律：\\[ \Gamma_{\cal O}[\Phi] = \operatorname*{Stat}_{\Psi} \left\{ \Gamma_{\cal C}[\Psi] + \Gamma_{\rm IF}[\Phi-\Psi] \right\} \\]其中${\rm Stat}$表示对$\Psi$求定态条件的解。该变分合成适用于非平衡量子场论中局域和非局域的施温格-凯尔迪什有效作用量，本文分别通过二次理论和一般时间无关的有效作用量，阐释其线性和非线性实现形式。
英文摘要
Let $W_{\cal O}[J]$ and $W_{\cal C}[J]$ denote the connected generating functionals of an open system and its closed system counterpart, and define the environment-induced contribution $W_{\rm IF}[J]$ by the difference: $ W_{\rm IF}[J]\equiv W_{\cal O}[J]-W_{\cal C}[J].$ The corresponding Legendre transforms, $Γ_{\cal O}$, $Γ_{\cal C}$, and $Γ_{\rm IF}$, do not obey an analogous additive relation but satisfy a stationary composition law given by: \[ Γ_{\cal O}[Φ] = \operatorname*{Stat}_Ψ \left\{ Γ_{\cal C}[Ψ] + Γ_{\rm IF}[Φ-Ψ] \right\} \] where ${\rm Stat}$ 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.
Comments22 pages
