论文标题
在功能性汉密尔顿 - 雅各比（Hamilton-Jacobi）和Schrödinger方程和功能重新归一化组上
On Functional Hamilton-Jacobi and Schrödinger Equations and Functional Renormalization Group
论文作者
论文摘要
功能性Hamilton-Jacobi（HJ）方程，全息重新归一化组（HRG）的中心方程，功能性Schrödinger方程和广义的Wilson-Polchinski（WP）方程，$ D $ -DIMENSINIal CORIDATE的功能性更高授予组（FRG）的中心方程（FRG）的中央方程（FRG）的形式（形式）（形式）。引入了全息标量字段$ \ varlambda $，而不是额外的坐标或FRG量表。额外的坐标（或比例）作为$ \ varlambda $的三角洲场或常数字段配置的幅度。给出了相应的绿色功能（GFS）的相应的差异方程层次结构的严格推导以及功能的集成公式。使用Integration公式，获得了用于翻译不变的两粒子GF的功能（$ \ varlambda $的任意配置）。对于$ \ varlambda $的delta-field和恒定字段配置，该解决方案将详细研究。简要讨论了两粒子GF的可分离溶液。然后，给出了量子HJ的严格推导以及功能性schrödinger方程以及半经典近似的连续性功能方程。提出了一种解决功能性Schrödinger方程的迭代程序。获得了$ \ varlambda $的Delta-Field配置上的各种GFS（两个层次结构）的翻译不变解决方案。在连续性方程和开放量子场系统的背景下，简要讨论了光电位。分析了WP功能的模式粗晶粒生长功能。为广义WP方程提出了一个近似方案。通过优化的调节器翻译不变溶液，分析得出了来自近似WP层次结构的两粒子和四粒子截肢的GF。
Functional Hamilton-Jacobi (HJ) equation, the central equation of the holographic renormalization group (HRG), functional Schrödinger equation, and generalized Wilson-Polchinski (WP) equation, the central equation of the functional renormalization group (FRG), are considered in $D$-dimensional coordinate and abstract (formal) spaces. Instead of extra coordinates or an FRG scale, a holographic scalar field $\varLambda$ is introduced. The extra coordinate (or scale) is obtained as the amplitude of delta-field or constant field configurations of $\varLambda$. A rigorous derivation of corresponding integro-differential equation hierarchies for Green functions (GFs) as well as the integration formula for functionals are given. Using the integration formula, the functional (arbitrary configuration of $\varLambda$) solution for the translation-invariant two-particle GF is obtained. For the delta-field and the constant field configurations of $\varLambda$ this solution is studied in detail. Separable solution for two-particle GF is briefly discussed. Then, rigorous derivation of the quantum HJ and the continuity functional equations from the functional Schrödinger equation as well as the semiclassical approximation are given. An iterative procedure for solving the functional Schrödinger equation is suggested. Translation-invariant solutions for various GFs (both hierarchies) on delta-field configuration of $\varLambda$ are obtained. In context of continuity equation and open quantum field systems an optical potential is briefly discussed. Modes coarse graining growth functional for WP functional is analyzed. An approximation scheme is proposed for the generalized WP equation. With an optimized regulator translation-invariant solutions for two-particle and four-particle amputated GFs from approximated WP hierarchy are found analytically.
