From c66c3bc73d5d627ec7051e9ada6316c98ae072e0 Mon Sep 17 00:00:00 2001
From: Justin Gassner <justin.gassner@mailbox.org>
Date: Wed, 29 May 2024 14:04:59 +0200
Subject: weiter

---
 preamble.tex | 81 +++++++++++++++++++++++++++++++++++++++++++++++++-----------
 1 file changed, 67 insertions(+), 14 deletions(-)

(limited to 'preamble.tex')

diff --git a/preamble.tex b/preamble.tex
index 35d94ad..8479b31 100644
--- a/preamble.tex
+++ b/preamble.tex
@@ -11,9 +11,12 @@
 \usepackage{amsmath,amsthm}
 \usepackage{mathtools}
 \usepackage[colon=literal]{unicode-math} % TODO get rid of this since it messes up math italic correction
-\usepackage{enumitem}
+\usepackage[inline]{enumitem}
+\usepackage{multicol}
 %\usepackage{graphicx}
+\usepackage{tikz}
 \usepackage{tcolorbox}
+%\usepackage{wrapfig}
 \usepackage[style=ext-alphabetic]{biblatex}
 \usepackage[intoc,refpage]{nomencl}
 \usepackage{makeidx}
@@ -81,8 +84,10 @@
 % ---------- amsmath
 \numberwithin{equation}{chapter}
 \DeclareMathOperator{\supp}{supp}
+\DeclareMathOperator{\diag}{diag}
 \DeclareMathOperator{\dom}{dom}
 \DeclareMathOperator{\ran}{ran}
+\DeclareMathOperator{\Span}{span}
 % extend amsmath's proof environment
 \NewDocumentEnvironment{myproof}{Ob}{\IfNoValueTF{#1}{\begin{proof}}{\begin{proof}[\proofname\ of \Cref{#1}]}}{\end{proof}}
 
@@ -99,6 +104,12 @@
 \DeclarePairedDelimiterX\innerp[2]{\langle}{\rangle}{#1,#2}
 \DeclarePairedDelimiterX\LorentzBF[2]{\lparen}{\rparen}{#1,#2}
 
+% ---------- enumitem
+\setlist[enumerate,1]{label=(\roman*),nosep,leftmargin=*,widest=ii}
+
+% ---------- tikz
+\usetikzlibrary{arrows.meta}
+
 % ---------- tcolorbox
 \tcbuselibrary{skins,theorems,breakable} % add breakable library?
 \tcbset{%
@@ -177,7 +188,9 @@
 
 % ---------- nomencl
 \makenomenclature
-\renewcommand*{\nomname}{List of Symbols}
+\renewcommand{\nomname}{List of Symbols}
+\renewcommand{\nompreamble}{\begin{multicols}{2}}
+\renewcommand{\nompostamble}{\end{multicols}}
 %\def\pagedeclaration#1{, \hyperlink{page.#1}{page\nobreakspace#1}}
 \def\pagedeclaration#1{, \hyperlink{page.#1}{#1}}
 
@@ -234,6 +247,7 @@
 % TODO Why does this not work?
 \renewcommand{\Re}{\operatorname{Re}}
 \renewcommand{\Im}{\operatorname{Im}}
+\newcommand{\Real}{\operatorname{Re}}
 \newcommand{\Imag}{\operatorname{Im}}
 
 % emphasis for defined terms
@@ -283,6 +297,7 @@
 \newcommand*{\BosonFockFinite}[1]{\mathcal{F}^{@0}_{\!\ts{s}}(#1)}
 \newcommand*{\FermionFock}[1]{\mathcal{F}_{\!\ts{s}}(#1)}
 \newcommand*{\FermionFockFinite}[1]{\mathcal{F}^{@0}_{\!\ts{s}}(#1)}
+\newcommand*{\FockVacuum}{\Omega}
 
 % Operators
 % ---------
@@ -320,27 +335,65 @@
 \newcommand{\defequal}{\overset{\text{\scriptsize def}}{=}}
 
 \newcommand*{\energydensity}{\varrho}
-\newcommand*{\fockvaccum}{\Omega}
 
 % Observable Algebras
 \newcommand*{\vNa}[1]{\mathcal{#1}}
 \newcommand*{\localalg}[1]{\vNa{R}(#1)}
 
+% Measure Theroy
+\newcommand*{\BorelSigmaAlgebra}[2][]{\mathfrak{B}\parens[#1]{#2}}
+
+% Lorentz and Poincaré groups, subgroups and connected components
+\newcommand*{\LorentzGroup}{\mathcal{L}}
+\newcommand*{\FullLorentzGroup}{\LorentzGroup}
+\newcommand*{\ProperLorentzGroup}{\LorentzGroup_{+}}
+\newcommand*{\OrthochronousLorentzGroup}{\LorentzGroup^{\uparrow}}
+\newcommand*{\OrthochorousLorentzGroup}{\LorentzGroup_0}
+\newcommand*{\ProperOrthochronousLorentzGroup}{\LorentzGroup_{+}^{\uparrow}}
+\newcommand*{\RestrictedLorentzGroup}{\ProperOrthochronousLorentzGroup}
+\newcommand*{\ImproperOrthochronousLorentzTransformations}{\LorentzGroup_{-}^{\uparrow}}
+\newcommand*{\ProperNonorthochronousLorentzTransformations}{\LorentzGroup_{+}^{\downarrow}}
+\newcommand*{\ImproperNonorthochronousLorentzTransformations}{\LorentzGroup_{-}^{\downarrow}}
+
+\newcommand*{\ComplexLorentzGroup}{\LorentzGroup(\CC)}
+\newcommand*{\FullComplexLorentzGroup}{\ComplexLorentzGroup}
+\newcommand*{\ProperComplexLorentzGroup}{\ProperLorentzGroup(\CC)}
+\newcommand*{\ImproperComplexLorentzTransformations}{\LorentzGroup_{-}(\CC)}
+
+\newcommand*{\PoincareGroup}{\mathcal{P}}
+\newcommand*{\FullPoincareGroup}{\PoincareGroup}
+\newcommand*{\ProperPoincareGroup}{\PoincareGroup_{\!+}}
+\newcommand*{\OrthochronousPoincareGroup}{\PoincareGroup^{\uparrow}}
+\newcommand*{\OrthochorousPoincareGroup}{\PoincareGroup_0}
+\newcommand*{\ProperOrthochronousPoincareGroup}{\PoincareGroup_{\!+}^{\uparrow}}
+\newcommand*{\RestrictedPoincareGroup}{\ProperOrthochronousPoincareGroup}
+\newcommand*{\ImproperOrthochronousPoincareTransformations}{\PoincareGroup_{\!-}^{\uparrow}}
+\newcommand*{\ProperNonorthochronousPoincareTransformations}{\PoincareGroup_{\!+}^{\downarrow}}
+\newcommand*{\ImproperNonorthochronousPoincareTransformations}{\PoincareGroup_{\!-}^{\downarrow}}
+
+\newcommand*{\ComplexPoincareGroup}{\PoincareGroup(\CC)}
+\newcommand*{\FullComplexPoincareGroup}{\ComplexPoincareGroup}
+\newcommand*{\ProperComplexPoincareGroup}{\ProperPoincareGroup(\CC)}
+\newcommand*{\ImproperComplexPoincareTransformations}{\PoincareGroup_{\!-}(\CC)}
+
+% Functional Analysis
+\newcommand*{\BoundedLinearOperators}[2][]{B\parens[#1]{#2}}
+\DeclareMathOperator*{\stronglim}{s-lim}
+\DeclareMathOperator*{\weaklim}{w-lim}
 
-\newcommand*{\FullLorentzGroup}{\mathcal{L}}
-\newcommand*{\ProperOrthochronousLorentzGroup}{\FullLorentzGroup_{+}^{\uparrow}}
-\newcommand*{\FullPoincareGroup}{\mathcal{P}}
-\newcommand*{\ProperOrthochronousPoincareGroup}{\FullPoincareGroup_{+}^{\uparrow}}
-
-% spacetime domains
+% spacetime regions
 \newcommand*{\spacetimeregion}[1]{\mathcal{#1}}
 \newcommand*{\rightwedge}{W_{\! R}}
 \newcommand*{\leftwedge}{W_{\! L}}
+\newcommand*{\OpenForwardCone}{V_+}
+\newcommand*{\ClosedForwardCone}{\bar{V}_+}
+\newcommand*{\OpenForwardTube}{T_+}
+\newcommand*{\ClosedForwardTube}{\bar{T}_+}
 
-\newcommand*{\todo}[1]{{\color{blue}TODO: #1}}
-\newcommand*{\question}[1]{{\color{blue}Question: #1}}
-\newcommand*{\info}[1]{{\color{blue}Info: #1}}
+% comments
+\newcommand*{\bluetext}[1]{{\color{blue}#1}}
+\newcommand*{\todo}[1]{\bluetext{TODO: #1}}
+\newcommand*{\question}[1]{\bluetext{Question: #1}}
+\newcommand*{\info}[1]{\bluetext{Info: #1}}
 
 \newcommand*{\operatorclosure}[1]{\overline{#1}}
-
-\DeclareMathOperator*{\stronglim}{s-lim}
-- 
cgit v1.2.3-70-g09d2

