PhD-Thesis_mainmatter.tex

% ************ Mainmatter ************ %
\mainmatter

% ****** Introduction ****** %
\chapter{Introduction}\label{chap:introduction}\IMRADlabel{introduction}
\input{introduction/introduction}

% ****** Theoretical background and methods ****** %
\chapter{Theoretical background and methods}\label{chap:methods}\IMRADlabel{methods}
In this chapter we introduce the theoretical background and the methods used throughout this work.

In \cref{sec:FRG} we begin with a discussion and summary of the key concepts of the \frg{}\footnote{%
	Sometimes also referred to as \erg{} due to the fact that its central \rg{} evolution equation, \viz{} the \frgEq{}, is formally an exact equation.
	This is in contrast to earlier non-perturbative \rg{} evolution equations, which often times included approximations.%
}, which we use as the main theoretical frame work to compute observables for the models and theories studied in this thesis.
The central equations of the \frg{} framework manifest as flow (conservation) equations, which we will discuss in general in \cref{sec:conservationLaws} with a special focus on \cfd{}.
In the subsequent \cref{sec:qcdModels} we give a brief introduction of \qcd{} as the fundamental theory of the strong interaction, which includes a discussion of \loefts{} and their emergence from \qcd{} in the \frg{} framework.
We conclude this chapter with \cref{sec:inhomogeneousPhases}, where we provide a concise introduction to inhomogeneous phases (condensates), focusing on computational challenges, employed methods, and selected literature results.

\input{frg/frg}
\input{hydro/hydro}
\input{qcd/qcd}
\input{inhomo/inhomo}

% ****** Models in zero dimensions ****** %
\chapter{Models in zero dimensions}\label{chap:zeroONSU2}\IMRADlabel{results}
\input{0d/0dintro}
\input{0d/0dqft}
\input{0d/0dON}
\input{0d/0dsu2model}
\input{0d/0dconclusion}

% ****** Gross-Neveu model in two dimensions ****** %
\chapter{Gross-Neveu model in two dimensions}\label{chap:GN}
\input{gn/GNintro}
\input{gn/gny}
\input{gn/gnyFRG}
\input{gn/gnInfNhomo}
\input{gn/gnInfNinhomo}
\input{gn/gnFiniteN}
\input{gn/gnConclusion}

% ****** Quark meson model in four dimensions ****** %
\chapter{Quark meson model in four dimensions}\label{chap:QMM}
\input{qmm/qmm}

% ****** Summary ****** %
\chapter{Summary and outlook}\label{chap:conclusion}\IMRADlabel{discussion}
\input{conclusion}

% ************ Appendices ************ %
\part*{Appendices}\label{app:app}
\appendix
\chapter{Digital auxiliary files and used software}
\input{appendix/auxFiles}
\input{appendix/software}

\chapter{Units, conventions, and notations}\label{app:conventions}%
\input{appendix/conventions}

\chapter{Thermal quantum field theory}\label{app:thermalQFT}
\input{appendix/thermalQFT}

\chapter{Models in zero dimensions}\label{app:zerod}
\input{appendix/zerod}

\chapter{Gross-Neveu model in two dimensions}\label{app:gn}
\input{appendix/gnApp}