272 lines
9.6 KiB
TeX
272 lines
9.6 KiB
TeX
\usepackage{amsmath}
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\usepackage{amssymb}
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\usepackage{mathtools}
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% \usepackage{esint}
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\usepackage{amsthm}
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\usepackage{framed}
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\usepackage{mathrsfs} %定义了类似铜版体的\mathscr
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%\usepackage{upgreek}
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%\usepackage{textcomp}
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\usepackage{physics}
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\usepackage{cancel}
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% \usepackage{geometry}
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%\usepackage{tabularx}
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\usepackage{hyperref}
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% \usepackage[amsmath,hyperref,thmmarks,framed]{ntheorem}
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%\usepackage{bookmark}
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\usepackage{xcolor}
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%\usepackage{graphicx}
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% \usepackage{enumitem}
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%\usepackage{fancyvrb}%能用颜文字卖萌了，2333
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%\usepackage{siunitx}%生成标准格式的国际单位
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\usepackage{tensor}
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\usepackage{tikz}
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%\usepackage{listings}
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%\usepackage{fontspec}
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%\usepackage{minted}
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%\usepackage{pifont}
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\usepackage{bm}
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% \usepackage{nomencl}
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\usepackage[backref=true]{biblatex}
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\hypersetup{
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colorlinks=true,
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linkcolor=blue,
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% pdftitle={Notes on Loop Quantum Gravity},
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pdfauthor={Yingjie Wang}
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}
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% {
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% \theoremstyle{plain}
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% \theoremsymbol{\ensuremath{\clubsuit}}
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% \theoremseparator{.}
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% \theoremprework{\bigskip\hrule\smallskip}
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% \theorempostwork{\smallskip\hrule\bigskip}
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% \newtheorem{Definition}{定义}
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% }
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% {
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% \theoremstyle{plain}
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% \theoremheaderfont{\normalfont\bfseries}
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% \theorembodyfont{\slshape}
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% \theoremsymbol{\ensuremath{\diamondsuit}}
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% \theoremseparator{.}
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% % \theoremprework{\bigskip\hrule}
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% % \theorempostwork{\hrule\bigskip}
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% \newtheorem{Theorem}{定理}
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% }
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% {
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% \theoremclass{Theorem}
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% \theoremstyle{plain}
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% % \theoremheaderfont{\normalfont\bfseries}
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% % \theorembodyfont{\slshape}
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% % \theoremsymbol{\ensuremath{\diamondsuit}}
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% % \theoremseparator{.}
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% % \theoremprework{\bigskip\hrule}
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% % \theorempostwork{\hrule\bigskip}
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% \newframedtheorem{fTheorem}{Theorem}
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% }
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% {
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% \theoremstyle{plain}
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% \theorembodyfont{\slshape}
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% \theoremsymbol{\ensuremath{\diamondsuit}}
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% \theoremseparator{.}
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% % \theoremprework{\bigskip\hrule}
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% % \theorempostwork{\hrule\bigskip}
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% \newtheorem{Property}{命题}[section]
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% }
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% {
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% \theoremstyle{plain}
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% \theorembodyfont{\slshape}
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% \theoremsymbol{\ensuremath{\diamondsuit}}
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% \theoremseparator{.}
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% \theoremprework{\bigskip\hrule}
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% \theorempostwork{\hrule\bigskip}
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% \newtheorem{lProperty}{Property}
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% }
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% {
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% \theoremclass{Property}
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% \theoremstyle{plain}
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% \newframedtheorem{fProperty}{Property}
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% }
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% {
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% \theoremstyle{plain}
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% % \theoremsymbol{\ensuremath{\heartsuit}}
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% \theoremindent0.5cm
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% % \theoremnumbering{greek}
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% \newtheorem{Lemma}{引理}
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% }
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% {
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% \theoremindent0cm
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% \theoremsymbol{\ensuremath{\spadesuit}}
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% \theoremnumbering{arabic}
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% \newtheorem{Corollary}[Theorem]{Corollary}
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% }
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% {
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% \theoremstyle{change}
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% \theorembodyfont{\upshape}
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% \theoremsymbol{\ensuremath{\ast}}
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% \theoremseparator{}
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% \newtheorem{Example}{Example}
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% }
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% {
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% \theoremheaderfont{\upshape\bfseries}
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% \theorembodyfont{\mdseries\itshape}
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% \theoremstyle{nonumberplain}
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% \theoremseparator{}
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% \theoremsymbol{\mbox{$\square$}}
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% \newtheorem{Proof}{证明}[section]
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% }
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% {
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% \theoremindent0cm
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% \theoremsymbol{\ensuremath{\spadesuit}}
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% \theoremnumbering{arabic}
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% \theorembodyfont{\upshape}
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% \newtheorem{Remark}{注}
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% }
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\newcommand{\myvec}[1]{\vb*{#1}} %定制矢量格式
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\newcommand{\myvu}[1]{\vu*{#1}}%单位矢量
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%\providecommand{\dd}[0]{\mathrm{d}}
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\newcommand{\qst}{\qq{s.t.}}
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\newcommand{\qsts}{\qq*{s.t.}}
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\newcommand{\tst}{\text{s.t.}}
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\newcommand{\RomanNumeralCaps}[1]{\textnormal{\MakeUppercase{\romannumeral #1}}}
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\newcommand{\e}[1]{\mathrm{e}^{#1}}
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\newcommand{\ii}{\mathrm{i}}
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\newcommand{\nG}{\ensuremath{\mathrm{G}}}
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\newcommand{\gkappa}{\upkappa}
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\newcommand{\dvt}[2][]{\dv[#1]{#2}{t}}
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\newcommand{\pdvt}[2][]{\pdv[#1]{#2}{t}}
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\newcommand{\pd}[1]{\pdv*{}{#1}}
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\newcommand{\liej}[1]{\ensuremath{{#1}_1,\cdots,{#1}_n}}
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\newcommand{\qqiff}{\qq{iff}}
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\newcommand{\F}{\ensuremath{\mathscr{F}}}
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\newcommand{\La}{\ensuremath{\mathscr{L}}}
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\newcommand{\Lad}{\ensuremath{\tilde{\mathscr{L}}}}
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\newcommand{\Laf}{\ensuremath{\form{L}}}
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\newcommand{\Ha}{\ensuremath{\mathscr{H}}}
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\newcommand{\Had}{\ensuremath{\tilde{\mathscr{H}}}}
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\newcommand{\Ld}[1]{\ensuremath{\mathcal{L}\indices{_{#1}}}}
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\newcommand{\spaceLd}[1]{\ensuremath{\tilde{\mathcal{L}}\indices{_{#1}}}}
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\newcommand{\TT}{\ensuremath{\mathscr{T}}}
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\newcommand{\I}{\ensuremath{\mathrm{I}}}
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\newcommand{\II}{\ensuremath{I}}
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\newcommand{\J}{\ensuremath{\mathrm{J}}}
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% \newcommand{\hj}[2][-1bp]{\raisebox{#1}{\includegraphics[height=#2 bp]{hj}}}
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% \newcommand{\wl}[2][-1bp]{\raisebox{#1}{\includegraphics[height=#2 bp]{wulian}}}
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\newcommand{\Nabla}[1]{\tensor{\nabla}{_{#1}}}%协变导数算符
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\newcommand{\tNabla}[1]{\tensor{{\tilde{\nabla}}}{_{#1}}}%另一个协变导数算符
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\newcommand{\spaceD}[1]{\tensor{D}{_{#1}}}
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\newcommand{\Dc}[1]{\tensor{D}{_{#1}}}
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\newcommand{\tDc}[1]{\tensor{\tilde{D}}{_{#1}}}
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\newcommand{\AD}[1]{\tensor{\mathcal{D}}{_{#1}}}
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\newcommand{\ADd}{\mathcal{D}}
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\newcommand{\connection}[1]{\mathcal{#1}}
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\newcommand{\Partial}[1]{\tensor{\partial}{_{#1}}}%普通导数算符
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\newcommand{\tPartial}[1]{\tensor{\tilde{\partial}}{_{#1}}}
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\newcommand{\Fd}[2][\tau]{\ensuremath{\frac{\mathrm{D_F}#2}{\dd{#1}}}}%费米导数
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\newcommand{\Fdd}[2][\tau]{\ensuremath{\mathrm{D_F}#2/\dd{#1}}}%行内费米导数
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\newcommand{\Dd}[2][\tau]{\ensuremath{\frac{\mathrm{D}#2}{\dd{#1}}}}%协变导数
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\newcommand{\Ddd}[2][\tau]{\ensuremath{\mathrm{D}#2/\dd{#1}}}%行内协变导数
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\newcommand{\ChristoffelSymbol}[3]{\tensor{\Gamma}{^{#1}_{#2}_{#3}}}
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\newcommand{\christoffelSymbol}[4]{\frac{1}{2} \tensor{g}{^{#1}^{#4}} \left( \tensor{g}{_{#4}_{#2}_{,#3}} + \tensor{g}{_{#3}_{#4}_{,#2}} - \tensor{g}{_{#2}_{#3}_{,#4}} \right) }
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\newcommand{\riemannR}[5]{\tensor{\Gamma}{^{#4}_{#1}_{#3}_{,#2}}- \tensor{\Gamma}{^{#4}_{#2}_{#3}_{,#1}}+ \ChristoffelSymbol{#5}{#3}{#1} \ChristoffelSymbol{#4}{#2}{#5}- \ChristoffelSymbol{#5}{#3}{#2} \ChristoffelSymbol{#4}{#1}{#5}}
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%\newcolumntype{Y}{>{\centering\arraybackslash}X}
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%\newcommand{\tmu}{\mspace{2mu}}
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%\newcommand{\mmacs}{\bfseries\ttfamily\itshape\color[RGB]{67,137,88}}%mma局部变量字体
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%\newcommand{\mmab}{\bfseries\ttfamily\color[RGB]{60,125,145}}%mma变量字体
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%\newcommand{\mmaundef}{\bfseries\ttfamily\color[RGB]{0,44,195}}%mma未定义
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%\newcommand{\mma}{\bfseries\ttfamily}%mma代码字体
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\newcommand{\tensord}[2]{\tensor{\left( \dd{#1} \right)}{_{#2}}}
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\newcommand{\tensorp}[2]{\tensor{\left( \pdv{#1} \right)}{^{#2}}}
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% \newcommand{\Rn}[1]{\ensuremath{\mathbb{R}^{#1}}}
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\newcommand{\SO}[1]{\ensuremath{\mathrm{SO}\left(#1\right)}}
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\newcommand{\SU}[1]{\ensuremath{\mathrm{SU}\left(#1\right)}}
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\newcommand{\OO}[1]{\ensuremath{\mathrm{O}\left(#1\right)}}
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\newcommand{\so}[1]{\ensuremath{\mathrm{so}\left( #1 \right)}}
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\newcommand{\su}[1]{\ensuremath{\mathrm{su}\left( #1 \right)}}
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\newcommand{\SL}[1]{\mathrm{SL}\left( #1 \right)}
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\newcommand{\sll}[1]{\mathrm{sl}\left( #1 \right)}
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\newcommand{\Ad}[1]{\mathrm{Ad}_{#1}}
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\newcommand{\Hom}[2]{\mathrm{Hom}\left( #1,#2 \right)}
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\newcommand{\Cyl}{\mathrm{Cyl}}
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\newcommand{\Lo}[1]{\ensuremath{\mathrm{Lor}\left(#1\right)}}
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\newcommand{\Riem}[1]{\ensuremath{\mathrm{Riem}\left( #1 \right)}}
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\newcommand{\superspace}[1]{\ensuremath{\mathcal{S}\left(#1\right)}}
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\newcommand{\Diff}[1]{\ensuremath{\mathrm{Diff}\left(#1\right)}}
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\newcommand{\definedby}{:=}
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\newcommand{\phasespace}[1]{\mathcal{#1}}
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\newcommand{\configurationspace}[1]{\mathcal{#1}}
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\newcommand{\extentedconfigurationspace}[1]{\bar{\configurationspace{#1}}}
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\newcommand{\staralgebra}[1]{\mathfrak{#1}}
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\newcommand{\Linear}[1]{\mathcal{L}\left( {#1} \right)}
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\newcommand{\pathorder}{\hat{\mathcal{P}}}
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\newcommand{\Dkin}{\mathcal{D}_{\text{kin}}}
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\newcommand{\DDiff}{\mathcal{D}_{\text{Diff}}}
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\newcommand{\Dphys}{\mathcal{D}_{\text{phys}}}
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\newcommand{\Hil}{\mathcal{H}}
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\newcommand{\Hkin}{\Hil_{\text{kin}}}
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\newcommand{\HDiff}{\Hil_{\text{Diff}}}
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\newcommand{\Hphys}{\Hil_{\text{phys}}}
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\newcommand{\masterconstraint}[1]{\ensuremath{\bm{\mathsf{#1}}}}
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\newcommand{\complex}[1]{\mathcal{#1}}
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\newcommand{\amplitude}{A}
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\newcommand{\form}[1]{\ensuremath{\bm{#1}}}
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\newcommand{\Ric}{\ensuremath{R}}
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\newcommand{\Rscalar}{\ensuremath{R}}
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\newcommand{\curR}{\ensuremath{{R}}}
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\newcommand{\spacecurR}{\ensuremath{\mathcal{R}}}
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\newcommand{\vol}{\ensuremath{\varepsilon}}
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\newcommand{\nvol}{\ensuremath{\epsilon}}
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\newcommand{\spc}{\ensuremath{\mathcal{S}}}
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\newcommand{\setofcurve}{\mathcal{C}}
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\newcommand{\setofpath}{\mathcal{P}}
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\newcommand{\TB}[2][{}]{\mathrm{T}_{#1}\!{#2}}
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\newcommand{\TBx}[2][{}]{\mathrm{T}_{#1} {#2}}
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\newcommand{\CTB}[2][{}]{\mathrm{T}^*_{#1}\!{#2}}
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\newcommand{\FB}[2][{}]{\mathrm{F}_{#1}\!{#2}}
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\newcommand{\Jet}[4][{}]{\ensuremath{\mathrm{Jet}_{#1}^{#2}\left( #3,#4 \right)}}
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\newcommand{\Cinf}{\mathrm{C}^{\infty}}
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\newcommand{\Vect}[1]{\Gamma\left(\TB{#1}\right)}
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\newcommand{\End}[1]{\mathrm{End}\left( #1 \right)}
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% \newcommand{\uphbar}{\mathchar'0026\mkern-9mu h}
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\newcommand{\uphbar}{\hbar}
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%\renewcommand{\CancelColor}{\color{blue!70!red}}
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%\newcommand*{\circled}[1]{\lower.7ex\hbox{\tikz\draw (0pt, 0pt)circle (.5em) node {\makebox[1em][c]{\small #1}};}}
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\newcommand{\card}[1]{\abs{#1}}
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\newcommand{\setR}{\mathbb{R}}
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\newcommand{\setC}{\mathbb{C}}
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\newcommand{\setZ}{\mathbb{Z}}
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\newcommand{\set}[2]{\left\{ #1 \,\middle|\, #2 \right\}}
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\newcommand{\RP}[1]{\mathbb{RP}^{#1}}
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\newcommand{\myvaried}[1]{{\phantom{#1}\llap{\raisebox{0pt}[0pt][0pt]{\ensuremath{\mspace{3mu}\overset{\lambda}{#1}}}}}}
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\DeclareMathOperator{\Span}{Span}
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\DeclareMathOperator{\Inv}{Inv}
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\DeclareMathOperator{\image}{im}
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% \usetheme{PaloAlto}
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% \usetheme{AnnArbor}
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%\usecolortheme{beaver}
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\usetheme{Darmstadt}
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\usefonttheme{professionalfonts}
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