%% Add to TOC
\phantomsection\label{sec:preliminaries}
\addcontentsline{toc}{chapter}{Preliminaries}
\chapter*{Preliminaries}

\subsubsection{Requirements for this course}

For this course, we assume that students are familiar with the following concepts:
%
\begin{itemize}
    \item Non-relativistic quantum mechanics and second quantization
    \item Lagrangian and Hamiltonian formalism of classical mechanics
    \item Special theory of relativity and tensor calculus
    \item Complex analysis (contour integrals, residue theorem, ...)
\end{itemize}


\subsubsection{Literature recommendations}

\begin{itemize}
    \item Weinberg: \textit{The Quantum Theory of Fields (Volume 1)} \cite{Weinberg1996}\\
        \texttt{ISBN 978-0-521-67053-1}\\
        {\small Standard reference, very rigorous \& mathematical, \#formulas/\#text = high}
    \item Itzykson \& Zuber: \textit{Quantum Field Theory} \cite{Itzykson2005}\\
        \texttt{ISBN 978-0-486-44568-7}\\
        {\small Standard reference, \#formulas/\#text = high}
    \item \textbf{Peskin \& Schroeder: \textit{An Introduction to Quantum Field Theory}} \cite{Peskin1995}\\
        \texttt{ISBN 978-0-201-50397-5}\\
        {\small Standard reference for courses on QFT, \#formulas/\#text = medium}
    \item Zee: \textit{Quantum Field Theory in a Nutshell} \cite{Zee2010}\\
        \texttt{ISBN 978-0-691-14034-6}\\
        {\small Compact and pedagogical introduction to the field, \#formulas/\#text = low}
\end{itemize}
%
For a first introduction to QFT, \emph{Peskin \& Schroeder} is a good choice
(which we will use in this course). Then, if you are hooked and want to
understand QFT in depth (in particular its mathematical foundations) read
\emph{Weinberg} afterwards.

\subsubsection{Goals of this course}

The goal of this course is to gain  a thorough understanding of relativistic
quantum field theory, the concepts of Feynman diagrams, renormalization for
quantum electrodynamics, and to extend this knowledge to non-abelian gauge
theories. In particular (\optional optional):
%
\begin{itemize}
    \item Relativistic quantum mechanics (Klein-Gordon and Dirac field)
    \item Quantization of free fields
    \item Perturbative analysis of interacting fields
    \item Feynman rules and diagrams
    \item Elementary processes and first corrections of quantum electrodynamics
    \item Renormalization
    \item Path integral formalism
    \item Non-abelian gauge fields \optional
    \item Spontaneous symmetry breaking and the Higgs mechanism \optional
    \item Structure of the Standard Model \optional
\end{itemize}
%
This course follows and partially covers Part I (field quantization,
perturbation theory, Feynman rules) and Part II (path integrals,
renormalization) of ``An Introduction to Quantum Field Theory'' by Peskin \&
Schroeder. If there is time, we close with a brief perspective on Part III
(non-abelian gauge theories, standard model).

\subsubsection{Notes on this document}

\begin{itemize}
    %
    \item This document is \textbf{not} an extension of the material covered
    in the lectures but the script that I use to prepare them. 
    %
    \item Please have a look at Peskin \& Schroeder for more comprehensive
    coverage; the corresponding pages are noted in the headers (→~PS:xx--yy).
    %
    \item The content of this script is color-coded as follows:
        %
        \begin{itemize}
            \item Text in black is written to the blackboard.
            \item \imp{Notes in red should be mentioned in the lecture to prevent misconceptions.}
            \item \note{Notes in blue can be mentioned/noted in the lecture if there is enough time.}
            \item \aside{Notes in green are hints for the lecturer.}
        \end{itemize}
    %
    \item One page of the script corresponds roughly to one covered panel of the blackboard.
    %
    \item Enumerated lists are used for more or less rigorous chains of thought:
        \begin{lot}
            \item This leads to \ldots
            \item this. By the way:
                \begin{lot}
                    \item This leads to \ldots
                    \item this leads to \ldots
                    \item this.
                \end{lot}
            \item Let's proceed \ldots
        \end{lot}
        %
\end{itemize}

\subsubsection{Acknowledgments}

\begin{itemize}
    \item \emph{Manya Willberg} translated some of my ugly sketches into nice TikZ figures.
    \item \emph{Johannes Mögerle} spotted various typos in the script.
\end{itemize}



\clearpage
\subsubsection{Key}

The following abbreviations and glyphs are used in this document:

{
    \renewcommand{\arraystretch}{1.5}
    \renewcommand{\arrayrulewidth}{1.5pt}
    \leavevmode
    \begin{tabular}{R{1.2cm} | l}
        \textit{cf}         & confer {\small(``compare'')} \\
        \textit{dof}        & degree(s) of freedom \\
        \textit{eg}         & exempli gratia {\small(``for example'')} \\
        \textit{etc}        & et cetera {\small(``and so forth'')} \\
        \textit{et al}      & et alii {\small(``and others'')} \\
        \textit{ie}         & id est {\small(``that is'')} \\
        \textit{viz}        & videlicet {\small(``namely'')} \\
        \textit{vs}         & versus {\small(``against'')} \\
        \textit{wlog}       & without loss of generality \\
        \textit{wrt}        & with respect to \\
        \consider           & ``consider'' \\
        \therefore          & ``therefore'' \\
        $\nte$              & non-obvious equality that may require lengthy, but straightforward calculations \\
        $\hnte$             & non-trivial equality that cannot be derived without additional input \\
        \easytoshow         & ``it is easy to show'' \\
        \noteasytoshow      & ``it is \emph{not} easy to show'' \\
        \limplies           & logical implication \\
        \land               & logical conjunction \\
        \lor                & logical disjunction \\
        $\rep$              & repeated expression \\
        $\aref$             & anonymous reference \\
        w/o                 & ``without'' \\
        w/                  & ``with'' \\
        \fref               & internal forward reference {\small(``see below/later'')} \\
        \bref               & internal backward reference {\small(``see above/before'')} \\
        \uref               & external reference to advanced concepts {\small(``have a look at an advanced textbook on\ldots'')} \\
        \dref               & external reference to basic concepts {\small(``remember your basic course on\ldots'')} \\
        (->)                & reference to previous or upcoming exercises \\
        \optional           & optional choice/item \\
        \termdef{}          & implicit or explicit definition of a new technical term \small(``so called \ldots'')
    \end{tabular}
}