Z2 规范理论

Reiko10/13/2020, 9:42:44 AM

%Abbreviations of Greek letters def \a {\alpha} def \b {\beta} def \g {\gamma} def \G {\Gamma} def \d {\delta} def \D {\Delta} def \e {\epsilon} def \ve {\varepsilon} def \m {\mu} def \n {\nu} def \k {\kappa} def \l {\lambda} def \L {\Lambda} def \s {\sigma} def \S {\Sigma} def \r {\rho} def \o {\omega} def \O {\Omega} def \th {\theta} def \Th {\Theta} def \t {\tau} def \z {\zeta} %Abbreviations of mathbb fonts newcommand{\R}{\mathbb{R}} newcommand{\N}{\mathbb{N}} newcommand{\Z}{\mathbb{Z}} newcommand{\C}{\mathbb{C}} newcommand{\V}{\mathbb{V}} %%vector spaces newcommand{\W}{\mathbb{W}} %%vector spaces %Abbreviations of Lie algebras newcommand{\glie}{\mathfrak{g}} %%generic Lie algebra newcommand{\gllie}{\mathfrak{gl}} %%general linear newcommand{\sllie}{\mathfrak{sl}} %%special linear newcommand{\solie}{\mathfrak{so}} %%special orthogonal newcommand{\splie}{\mathfrak{sp}} %%symplectic newcommand{\nlie}{\mathfrak{n}} %%nilpotent or solvable algebra newcommand{\plie}{\mathfrak{p}} %%nilpotent or solvable algebra newcommand{\hlie}{\mathfrak{h}} %%abelian factor newcommand{\klie}{\mathfrak{k}} %%maximal compact subalgebra newcommand{\blie}{\mathfrak{b}} %%Borel subalgebra %Others newcommand{\greenfunction}[1]{\langle #1\rangle} %%green functions renewcommand{\vev}[1]{\langle #1\rangle} %%green functions renewcommand{\H}{\mathcal{H}} %%Hilbert spaces newcommand{\Ccat}{\mathcal{C}} %%categories newcommand{\Acat}{\mathcal{A}} %%categories newcommand{\Bcat}{\mathcal{B}} %%categories newcommand{\p}{\partial} %%partial derivatives newcommand{\nn}{\nonumber} %due to old version of MathJax newcommand{\set}[1]{{#1}} newcommand{\ket}[1]{\vert #1 \rangle}

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分形子模型

Reiko10/13/2020, 11:22:17 AM

%Abbreviations of Greek letters def \a {\alpha} def \b {\beta} def \g {\gamma} def \G {\Gamma} def \d {\delta} def \D {\Delta} def \e {\epsilon} def \ve {\varepsilon} def \m {\mu} def \n {\nu} def \k {\kappa} def \l {\lambda} def \L {\Lambda} def \s {\sigma} def \S {\Sigma} def \r {\rho} def \o {\omega} def \O {\Omega} def \th {\theta} def \Th {\Theta} def \t {\tau} def \z {\zeta} %Abbreviations of mathbb fonts newcommand{\R}{\mathbb{R}} newcommand{\N}{\mathbb{N}} newcommand{\Z}{\mathbb{Z}} newcommand{\C}{\mathbb{C}} newcommand{\V}{\mathbb{V}} %%vector spaces newcommand{\W}{\mathbb{W}} %%vector spaces %Abbreviations of Lie algebras newcommand{\glie}{\mathfrak{g}} %%generic Lie algebra newcommand{\gllie}{\mathfrak{gl}} %%general linear newcommand{\sllie}{\mathfrak{sl}} %%special linear newcommand{\solie}{\mathfrak{so}} %%special orthogonal newcommand{\splie}{\mathfrak{sp}} %%symplectic newcommand{\nlie}{\mathfrak{n}} %%nilpotent or solvable algebra newcommand{\plie}{\mathfrak{p}} %%nilpotent or solvable algebra newcommand{\hlie}{\mathfrak{h}} %%abelian factor newcommand{\klie}{\mathfrak{k}} %%maximal compact subalgebra newcommand{\blie}{\mathfrak{b}} %%Borel subalgebra %Others newcommand{\greenfunction}[1]{\langle #1\rangle} %%green functions renewcommand{\vev}[1]{\langle #1\rangle} %%green functions renewcommand{\H}{\mathcal{H}} %%Hilbert spaces newcommand{\Ccat}{\mathcal{C}} %%categories newcommand{\Acat}{\mathcal{A}} %%categories newcommand{\Bcat}{\mathcal{B}} %%categories newcommand{\p}{\partial} %%partial derivatives newcommand{\nn}{\nonumber} %due to old version of MathJax newcommand{\set}[1]{{#1}}

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Shadow formalism

Reiko10/14/2020, 1:37:52 PM

%Abbreviations of Greek letters def \a {\alpha} def \b {\beta} def \g {\gamma} def \G {\Gamma} def \d {\delta} def \D {\Delta} def \e {\epsilon} def \ve {\varepsilon} def \m {\mu} def \n {\nu} def \k {\kappa} def \l {\lambda} def \L {\Lambda} def \s {\sigma} def \S {\Sigma} def \r {\rho} def \o {\omega} def \O {\Omega} def \th {\theta} def \Th {\Theta} def \t {\tau} def \z {\zeta} %Abbreviations of mathbb fonts newcommand{\R}{\mathbb{R}} newcommand{\N}{\mathbb{N}} newcommand{\Z}{\mathbb{Z}} newcommand{\C}{\mathbb{C}} newcommand{\V}{\mathbb{V}} %%vector spaces newcommand{\W}{\mathbb{W}} %%vector spaces %Abbreviations of Lie algebras newcommand{\glie}{\mathfrak{g}} %%generic Lie algebra newcommand{\gllie}{\mathfrak{gl}} %%general linear newcommand{\sllie}{\mathfrak{sl}} %%special linear newcommand{\solie}{\mathfrak{so}} %%special orthogonal newcommand{\splie}{\mathfrak{sp}} %%symplectic newcommand{\nlie}{\mathfrak{n}} %%nilpotent or solvable algebra newcommand{\hlie}{\mathfrak{h}} %%abelian factor newcommand{\klie}{\mathfrak{k}} %%maximal compact subalgebra newcommand{\blie}{\mathfrak{b}} %%Borel subalgebra %Others %\newcommand{\bra}[1]{\langle #1 \vert} %\newcommand{\ket}[1]{\vert #1 \rangle} %\newcommand{\braket}[2]{\langle #1\vert #2\rangle} %\newcommand{\greenfunction}[1]{\langle #1\rangle} %%green functions newcommand{\vev}[1]{\langle #1\rangle} %%green functions renewcommand{\H}{\mathcal{H}} %%Hilbert spaces newcommand{\Ccat}{\mathcal{C}} %%categories newcommand{\Acat}{\mathcal{A}} %%categories newcommand{\Bcat}{\mathcal{B}} %%categories newcommand{\p}{\partial} %%partial derivatives newcommand{\nn}{\nonumber} %Abbreviations of Lie algebras newcommand{\glie}{\mathfrak{g}} %%generic Lie algebra newcommand{\gllie}{\mathfrak{gl}} %%general linear newcommand{\sllie}{\mathfrak{sl}} %%special linear newcommand{\solie}{\mathfrak{so}} %%special orthogonal newcommand{\splie}{\mathfrak{sp}} %%symplectic newcommand{\nlie}{\mathfrak{n}} %%nilpotent or solvable algebra newcommand{\hlie}{\mathfrak{h}} %%abelian factor newcommand{\klie}{\mathfrak{k}} %%maximal compact subalgebra newcommand{\blie}{\mathfrak{b}} %%Borel subalgebra Shadow transform as an intertwining operator to be added Shadow transform from momentum space Gillioz, Momentum-space conformal blocks on the ight cone 这篇文章讨论如何通过动量空间的完备关系来得到shadow transform。下面我会通过1d CFT的计算来展示这个过程。 一般性的讨论 1d OPE代数, begin{equation} \phi_{i}\left(x_{1}\right) \phi_{j}\left(x_{2}\right)=\sum_{k} c_{i j}^{k} D_{i j}^{k}\left(x_{1}, x_{2},\p_2\right) \phi_{k}\left(x_{2}\right) end{equation} 平移的作用下不是平凡的, D_{i j}^{k}\left(x_{1}, x_{2},\p_2\right)=\frac{1}{|x_{12}|^{\D_{i}+\D_{j}-\D_{k}}}F_{11}\left(\D_{i}-\D_{j}+\D_{k}, 2 \D_{k} ; x_{12} \partial_{2}\right)]

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Knapp's book on semisimple groups

Reiko10/14/2020, 11:18:35 PM

newcommand{\set}[1]{{#1}} newcommand{\dd}[1]{\mathrm{d} #1 } newcommand{\pdv}[2]{\frac{\partial #1}{\partial #2}} Same as in Markdown. Abbreviations of Greek letters renewcommand{\a}{\alpha} renewcommand{\b}{\beta} newcommand{\g}{\gamma} newcommand{\G}{\Gamma} renewcommand{\d}{\delta} newcommand{\D}{\Delta} newcommand{\e}{\epsilon} newcommand{\ve}{\varepsilon} newcommand{\m}{\mu} newcommand{\n}{\nu} renewcommand{\k}{\kappa} renewcommand{\l}{\lambda} renewcommand{\L}{\Lambda} newcommand{\s}{\sigma} renewcommand{\S}{\Sigma} renewcommand{\r}{\rho} renewcommand{\o}{\omega} renewcommand{\O}{\Omega} renewcommand{\th}{\theta} newcommand{\Th}{\Theta} renewcommand{\t}{\tau} newcommand{\z}{\zeta} Abbreviations of mathbb fonts newcommand{\mbf}{\mathbf} newcommand{\mb}{\mathbb} newcommand{\mc}{\mathcal} newcommand{\mf}{\mathfrak} newcommand{\R}{\mathbb{R}} newcommand{\N}{\mathbb{N}} newcommand{\Z}{\mathbb{Z}} newcommand{\C}{\mathbb{C}} newcommand{\V}{\mathbb{V}} \newcommand{\W}{\mathbb{W}} % Abbreviations of mathcal fonts newcommand{\cP}{\mathcal P} newcommand{\cO}{\mathcal O} newcommand{\cA}{\mathcal A} newcommand{\cB}{\mathcal B} newcommand{\cC}{\mathcal C} newcommand{\cD}{\mathcal D} newcommand{\cH}{\mathcal H} newcommand{\cL}{\mathcal L} Abbreviations of Lie algebras newcommand{\glie}{\mathfrak{g}} %%generic Lie algebra newcommand{\gllie}{\mathfrak{gl}} %%general linear newcommand{\sllie}{\mathfrak{sl}} %%special linear newcommand{\solie}{\mathfrak{so}} %%special orthogonal newcommand{\splie}{\mathfrak{sp}} %%symplectic newcommand{\nlie}{\mathfrak{n}} %%nilpotent or solvable algebra newcommand{\plie}{\mathfrak{p}} %%nilpotent or solvable algebra newcommand{\hlie}{\mathfrak{h}} %%abelian factor newcommand{\klie}{\mathfrak{k}} %%maximal compact subalgebra newcommand{\blie}{\mathfrak{b}} %%Borel subalgebra Others newcommand{\greenfunction}[1]{\langle #1\rangle} % green functions renewcommand{\vev}[1]{\langle #1\rangle} \newcommand{\p}{\partial} % partial derivatives renewcommand{\inf}{\infty} % Infinity newcommand{\nn}{\nonumber} newcommand{\Diff}{\operatorname{Diff}} newcommand{\Aut}{\operatorname{Aut}} newcommand{\Ind}{\operatorname{Ind}} DeclareMathOperator{\sign}{sign} renewcommand{\hbar}{\bar{h}} newcommand{\zbar}{\bar{z}} newcommand{\integral}[3][]{\int_{#3}\dd[#1]{#2}} rep: representation, module irrep: irreducible representation spec: spectrum

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Neural Networks and QFT

Reiko1/21/2021, 3:51:19 PM

newcommand{\set}[1]{{#1}} newcommand{\pdv}[2]{\frac{\partial #1}{\partial #2}} newcommand{\myalign}[1]{\begin{aligned}#1\end{aligned}} newcommand{\myarray}[2]{\begin{array}{#1}#2\end{array}} renewcommand{\vev}[1]{\langle #1\rangle} newcommand{\p}{\partial} newcommand{\n}{\nabla} renewcommand{\inf}{\infty} newcommand{\Diff}{\operatorname{Diff}} newcommand{\Aut}{\operatorname{Aut}} newcommand{\End}{\operatorname{End}} newcommand{\Ind}{\operatorname{Ind}} newcommand{\sign}{\operatorname{sign}} renewcommand{\hbar}{\bar{h}} newcommand{\wbar}{\bar{w}} newcommand{\zbar}{\bar{z}} renewcommand{\a}{\alpha} renewcommand{\b}{\beta} newcommand{\g}{\gamma} newcommand{\G}{\Gamma} renewcommand{\d}{\delta} newcommand{\D}{\Delta} newcommand{\e}{\epsilon} newcommand{\ve}{\varepsilon} renewcommand{\k}{\kappa} renewcommand{\l}{\lambda} renewcommand{\L}{\Lambda} newcommand{\s}{\sigma} renewcommand{\S}{\Sigma} renewcommand{\r}{\rho} renewcommand{\o}{\omega} renewcommand{\O}{\Omega} renewcommand{\th}{\theta} newcommand{\Th}{\Theta} renewcommand{\t}{\tau} newcommand{\z}{\zeta} newcommand{\mbf}[1]{\mathbf{#1}} newcommand{\mb}[1]{\mathbb{#1}} newcommand{\mc}[1]{\mathcal{#1}} newcommand{\mf}[1]{\mathfrak{#1}} newcommand{\R}{\mathbb{R}} newcommand{\N}{\mathbb{N}} newcommand{\Z}{\mathbb{Z}} newcommand{\C}{\mathbb{C}} newcommand{\V}{\mathbb{V}} newcommand{\W}{\mathbb{W}} newcommand{\cP}{\mathcal{P}} newcommand{\cO}{\mathcal{O}} newcommand{\cA}{\mathcal{A}} newcommand{\cB}{\mathcal{B}} newcommand{\cC}{\mathcal{C}} newcommand{\cD}{\mathcal{D}} newcommand{\cH}{\mathcal{H}} newcommand{\cL}{\mathcal{L}} newcommand{\glie}{\mathfrak{g}} newcommand{\gllie}{\mathfrak{gl}} newcommand{\sllie}{\mathfrak{sl}} newcommand{\olie}{\mathfrak{o}} newcommand{\solie}{\mathfrak{so}} newcommand{\isolie}{\mathfrak{iso}} newcommand{\splie}{\mathfrak{sp}} newcommand{\nlie}{\mathfrak{n}} newcommand{\plie}{\mathfrak{p}} newcommand{\blie}{\mathfrak{b}} newcommand{\hlie}{\mathfrak{h}} newcommand{\klie}{\mathfrak{k}}

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文章名字至少要十个字

Reiko10/14/2020, 10:48:18 PM

这个帖子存放一些技巧。 Markdown 和 LaTeX 的相互转换问题目前没有很好的解决方案。 在 MathJax 中启用一些包的方式为 \require{},其支持的包可见 MathJax 文档 。 关于 MathJax 的一些介绍可见 SE 的帖子。 Markdown 基础语法可见 Markdown 中文文档。 交换图的绘制, LaTeX 中我用 tikz-cd 和 tikz 在线编辑器画简单的图,MathJax 的待补充,我好像看到 Colliot 有介绍。 physics package 文档 基于 AxoDraw 的绘图界面 JaxoDraw,优点是绘图中兼容 LaTeX,缺点是 UI 太老,功能单一。 尤亦庄写的一个常见包的推荐。 放弃 Lyx 和 Typora。

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Saddle point近似

Reiko11/3/2020, 7:23:59 PM

.

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【翻译】Wilson《重整化群和epsilon展开》

Reiko10/13/2020, 11:13:31 AM

二十多年来AdS/CFT和十年多年来Conformal Bootstrap的进展极大的加深了我们对于非微扰物理的理解,而这或多或少起源于有效理论的范式在各个物理领域中的实践。有效理论的应用依然在拓宽,另一方面在中文区相关的资源似乎并不够充足。因此译者想翻译这方面的始祖文章之一,Wilson的《重整化群和\epsilon展开》,另一篇被翻译的相关的简短介绍是《重整化群和临界现象》。 译者第一次尝试翻译,人名不翻译,一些在文献中第一次出现的名词会用括号标注,初稿可能跳过一些不想翻译的段落,以后逐步完善。 重整化群和epsilon展开 Kenneth G. Wilson, J. Kogut 目录 介绍 重整化群和物理中的连贯性问题 目前的一些参考文献 Ising模型的一些基本结论 a 系统在临界温度附近的基本性质 对解析性的探寻:1. 平均场理论;2. Kadanoff理论 重整化群的平凡例子:Gauss型模型 s^4模型 .简化版的重整化群变换 \epsilon展开和一个非平凡的不动点 线性化方程和对\nu的计算 s^4模型(续) 无关变量和\epsilon展开 完整的重整化群变换 近似的递推公式 Polyakov的推导 一些数值结果 a 关于近似递推公式进一步的结果 自旋n点函数的标度定理 slow transients和对\epsilon的消除 临界指数的Feynman图计算(\epsilon展开) 在4-\epsilon维时空中张量算子的量纲 统计力学和场论的联系 精确重整化群的微分形式 a 重整化群变换的拓扑(不动点,轨迹和子空间) 不动点,子空间和重整化 多不动点,区域和普适性 不动点和反常量纲 目前为止对4维\phi^4理论非平凡不动点的徒劳探寻 结语 致谢附录:精确重整化群方程的简单解参考文献

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Zettl's book on Sturm-Liouville problem

Reiko10/13/2020, 11:27:40 AM

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现在可以编辑帖子本身啦!

Colliot10/14/2020, 12:35:25 PM

这个「编辑」按钮终于不再是摆设!

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