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main.tex
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\documentclass[a4paper,11pt]{article}
\pdfoutput=1 % if your are submitting a pdflatex (i.e. if you have
% images in pdf, png or jpg format)
\usepackage{imakeidx}
\indexsetup{firstpagestyle=empty}
\makeindex[intoc, columns=2, title=Alphabetical Index, options= -s example_style.ist]
\usepackage{jheppub} % for details on the use of the package, please
% see the JHEP-author-manual
\usepackage[T1]{fontenc} % if needed
\usepackage{graphicx} % Required for including images
\graphicspath{{Figures/}} % Set the default folder for images
\usepackage{relsize} % for resizing maths relations
\usepackage{enumitem} % Required for manipulating the whitespace between and within lists
\usepackage{subfig} % Required for creating figures with multiple parts (subfigures)
\usepackage{stmaryrd}
\usepackage{amsmath,amssymb,amsthm,mathrsfs,amsfonts,xfrac,pifont} % For including math equations, theorems, symbols, etc
\usepackage{cleveref} % More descriptive referencing
%page margins and paragraph indentation
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%\geometry{a4paper,hmarginratio=1:1}
%\setlength{\parindent}{0pt}
%fonts
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%\usepackage{libertine}
%\usepackage[libertine]{newtxmath}
\usepackage{array,tabularx}
\usepackage[retainorgcmds]{IEEEtrantools}
\usepackage{etoolbox}
%\usepackage{mathtools}
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%----------------------------------------------------------------------------------------
% THEOREM STYLES
%---------------------------------------------------------------------------------------
%\newtheoremstyle{dotless}{}{}{\itshape}{}{\bfseries}{}{ }{}
%\theoremstyle{dotless}
\theoremstyle{definition} % Define theorem styles here based on the definition style (used for definitions and examples)
\newtheorem*{definition}{Definition}
\theoremstyle{plain} % Define theorem styles here based on the plain style (used for theorems, lemmas, propositions)
\newtheorem{theorem}{Theorem}[section]
\newtheorem{corollary}[theorem]{Corollary}
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{proposition}[theorem]{Proposition}
\theoremstyle{remark} % Define theorem styles here based on the remark style (used for remarks and notes)
\newtheorem{example}[theorem]{Example}
\newtheorem*{notation}{Notation}
\newtheorem{remark}[theorem]{Remark}
\newtheorem*{solution}{Solution}
%----------------------------------------------------------------------------------------
% HYPERLINKS
%---------------------------------------------------------------------------------------
%clever cross-references
%\usepackage[noabbrev,capitalize]{cleveref}
\usepackage{hyperref}
\hypersetup{
%draft, % Uncomment to remove all links (useful for printing in black and white)
colorlinks=true, linkcolor=black, breaklinks=true,
linktoc=all,
bookmarks=true,bookmarksnumbered=true,
%urlcolor=webbrown, linkcolor=RoyalBlue, citecolor=webgreen, % Link colors
pdftitle={}, % PDF title
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pdfencoding=unicode, %
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}
%dotted lines in contents
%\renewcommand{\cftsecleader}{\cftdotfill{\cftdotsep}}
\input{shortcuts}
\title{\boldmath Lectures on the Geometric Anatomy\\of Theoretical Physics}
%% %simple case: 2 authors, same institution
\author{Dr Frederic P. Schuller}
%\author{Simon Rea}
\affiliation{Friedrich-Alexander-Universit\"at Erlangen-N\"urnberg,\\Institut f\"ur Theoretische Physik III}
% more complex case: 4 authors, 3 institutions, 2 footnotes
%\author[a,b,1]{F. Irst,\note{Corresponding author.}}
%\author[c]{S. Econd,}
%\author[a,2]{T. Hird\note{Also at Some University.}}
%\author[a,2]{and Fourth}
% The "\note" macro will give a warning: "Ignoring empty anchor..."
% you can safely ignore it.
%\affiliation[a]{One University,\\some-street, Country}
%\affiliation[b]{Another University,\\different-address, Country}
%\affiliation[c]{A School for Advanced Studies,\\some-location, Country}
% e-mail addresses: one for each author, in the same order as the authors
\emailAdd{[email protected]}
%\emailAdd{[email protected]}
%\emailAdd{[email protected]}
%\emailAdd{[email protected]}
\pgfplotsset{compat=1.14}
\begin{document}
\rule{0cm}{2cm}\\
\includegraphics[width=14cm]{faulogo}
\maketitle
\section*{Introduction}
\addcontentsline{toc}{section}{Introduction}
\markright{Introduction}
\input{ga/00intro}
\newpage
\section{Logic of propositions and predicates}
\input{ga/01logic}
\newpage
\section{Axioms of set theory}
\input{ga/02axioms}
\newpage
\section{Classification of sets}
\input{ga/03classification}
\newpage
\section{Topological spaces: construction and purpose}
\input{ga/04topology}
\newpage
\section{Topological spaces: some heavily used invariants}
\input{ga/05topology_inv}
\newpage
\section{Topological manifolds and bundles}
\input{ga/06manifolds}
\newpage
\section{Differentiable structures: definition and classification}
\input{ga/07differentiable}
\newpage
\section{Tensor space theory I: over a field}
\input{ga/08tensor_i}
\newpage
\section{Differential structures: the pivotal concept of tangent vector spaces}
\input{ga/09tangent_space}
\newpage
\section{Construction of the tangent bundle}
\input{ga/10tangent_bundle}
\newpage
\section{Tensor space theory II: over a ring}
\input{ga/11tensor_ii}
\newpage
\section{Grassmann algebra and de Rham cohomology}
\input{ga/12grassmann}
\newpage
\section{Lie groups and their Lie algebras}
\input{ga/13lie_groups}
\newpage
\section{Classification of Lie algebras and Dynkin diagrams}
\input{ga/14classification}
\newpage
\section{The Lie group \texorpdfstring{$\SL(2,\C)$}{SL(2,C)} and its Lie algebra \texorpdfstring{$\sl(2,\C)$}{sl(2,C)}}
\input{ga/15sl2}
\newpage
\section{Dynkin diagrams from Lie algebras, and vice versa}
\input{ga/16dynkin}
\newpage
\section{Representation theory of Lie groups and Lie algebras}
\input{ga/17representation}
\newpage
\section{Reconstruction of a Lie group from its algebra}
\input{ga/18reconstruction}
\newpage
\section{Principal fibre bundles}
\input{ga/19principal}
\newpage
\section{Associated fibre bundles}
\input{ga/20associated}
\newpage
\section{Connections and connection 1-forms}
\input{ga/21connections}
\newpage
\section{Local representations of a connection on the base manifold: Yang-Mills fields}
\input{ga/22yang-mills}
\newpage
\section{Parallel transport}
\input{ga/23parallel}
\newpage
\section{Curvature and torsion on principal bundles}
\input{ga/24curvature}
\newpage
\section{Covariant derivatives}
\input{ga/25covariant}
\newpage
\setcounter{section}{25}
\section{Application: Quantum mechanics on curved spaces}
\input{ga/26quantum}
\newpage
\section{Application: Spin structures}
\input{ga/27spin}
\newpage
\section{Application: Kinematical and dynamical symmetries}
\input{ga/28kinematical}
\newpage
\section*{Further readings}
\addcontentsline{toc}{section}{Further readings}
\input{biblio}
\printindex
\end{document}