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Progress on fermions with defects

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Signed-off-by: Riccardo Finotello <riccardo.finotello@gmail.com>
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Riccardo
2020-09-29 18:48:42 +02:00
parent 5f7a0f734f
commit c47dd39f25
8 changed files with 2609 additions and 404 deletions
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66
thesis.tex
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@@ -23,64 +23,46 @@
pdfauthor={Riccardo Finotello}
}
%---- additional commands
\newcommand{\sm}{\textsc{sm}\xspace}
\newcommand{\eom}{\textsc{e.o.m.}\xspace}
\newcommand{\cft}{\textsc{cft}\xspace}
\newcommand{\ope}{\textsc{ope}\xspace}
\newcommand{\ap}{\ensuremath{\alpha'}}
\newcommand{\cy}{\textsc{CY}\xspace}
%---- functions
\newcommand{\hyp}[4]{\ensuremath{\mathrm{F}\left( #1,\, #2;\, #3;\, #4 \right)}}
\newcommand{\poch}[2]{\ensuremath{\left( #1 \right)_{#2}}}
\newcommand{\gfun}[1]{\ensuremath{\Gamma\left( #1 \right)}}
%---- derivatives
\newcommand{\pd}{\ensuremath{\partial}}
\newcommand{\bpd}{\ensuremath{\overline{\partial}}}
\newcommand{\lrpartial}[1]{\overset{\leftrightarrow}
{\partial_{ #1 }}
}
\newcommand{\consprod}[2]{\left\langle #1, #2 \right\rangle}
\newcommand{\lconsprod}[2]{\left\langle\hspace{-0.25em}\left\langle #1\right.,\, #2 \right\rangle}
\newcommand{\lfdv}[2]{\frac{\overset{\leftarrow}{\delta} #1}{\delta #2}}
\newcommand{\rfdv}[2]{\frac{\overset{\rightarrow}{\delta} #1}{\delta #2}}
\newcommand{\dual}[1]{\tensor[^*]{#1}{}}
%---- integrals
\newcommand{\ddz}{\ensuremath{\frac{\mathrm{d}z}{2 \pi i}}}
\newcommand{\ddbz}{\ensuremath{\frac{\mathrm{d}\overline{z}}{2 \pi i}}}
\newcommand{\ddw}{\ensuremath{\frac{\mathrm{d}w}{2 \pi i}}}
\newcommand{\ddbw}{\ensuremath{\frac{\mathrm{d}\overline{w}}{2 \pi i}}}
\newcommand{\cint}[1]{\ensuremath{\oint\limits_{\ccC_{#1}}}}
%---- operators
\newcommand{\bT}{\ensuremath{\overline{T}}}
\newcommand{\bL}{\ensuremath{\overline{L}}}
%---- states
\newcommand{\regvacuum}{\ensuremath{\ket{0}_{\SL{2}{R}}}}
\newcommand{\regvacuum}{\ensuremath{\ket{0}_{\SL{2}{R}}}\xspace}
\newcommand{\regvacuumin}{\ensuremath{\ket{0_{(\text{in})}}_{\SL{2}{R}}}\xspace}
\newcommand{\regvacuumout}{\ensuremath{\ket{0_{(\text{out})}}_{\SL{2}{R}}}\xspace}
\newcommand{\twsvacket}{\ensuremath{\ket{\mathrm{T}}}\xspace}
\newcommand{\twsvacbra}{\ensuremath{\bra{\mathrm{T}}}\xspace}
\newcommand{\excvacket}{\ensuremath{\ket{T_{\rE,\, \brE}}}\xspace}
\newcommand{\excvacbra}{\ensuremath{\bra{T_{\rE,\, \brE}}}\xspace}
\newcommand{\eexcvacket}{\ensuremath{\ket{T_{\rE}}}\xspace}
\newcommand{\eexcvacbra}{\ensuremath{\bra{T_{\rE}}}\xspace}
\newcommand{\Gexcvac}{\Omega_{\qty{x_{(t)},\, \rE_{(t)},\, \brE_{(t)}}}}
\newcommand{\Gexcvacket}{\ket{\Gexcvac}}
\newcommand{\Gexcvacbra}{\bra{\Gexcvac}}
\newcommand{\GGexcvac}{\Omega_{\qty{x_{(t)},\, \rE_{(t)}}}}
\newcommand{\GGexcvacket}{\ket{\GGexcvac}}
\newcommand{\GGexcvacbra}{\bra{\GGexcvac}}
\newcommand{\cmode}[4]{\mathfrak{C}_{#1}\qty(#2,\, \qty{#4,\, #3})}
%---- operators
\newcommand{\noE}[1]{\ccN_{\rE,\, \brE}\qty[ #1 ]}
%---- coordinates
\newcommand{\dX}{\ensuremath{\dot{X}}}
\newcommand{\pX}{\ensuremath{X'}}
\newcommand{\bX}{\ensuremath{\overline{X}}}
\newcommand{\bpsi}{\ensuremath{\overline{\psi}}}
\newcommand{\bxi}{\ensuremath{\overline{\xi}}}
\newcommand{\bchi}{\ensuremath{\overline{\chi}}}
\newcommand{\bz}{\ensuremath{\overline{z}}}
\newcommand{\bu}{\ensuremath{\overline{u}}}
\newcommand{\bt}{\ensuremath{\overline{t}}}
\newcommand{\bw}{\ensuremath{\overline{w}}}
\newcommand{\bomega}{\ensuremath{\overline{\omega}}}
\newcommand{\bepsilon}{\ensuremath{\overline{\epsilon}}}
\newcommand{\balpha}{\ensuremath{\overline{\alpha}}}
\newcommand{\bzeta}{\ensuremath{\overline{\zeta}}}
\newcommand{\halpha}{\ensuremath{\widehat{\alpha}}}
\newcommand{\hbeta}{\ensuremath{\widehat{\beta}}}
\newcommand{\htau}{\ensuremath{\widehat{\tau}}}
\newcommand{\hpsi}{\ensuremath{\widehat{\psi}}}
\newcommand{\Hpsi}{\ensuremath{\widehat{\Psi}}}
\newcommand{\pX}{\ensuremath{X'}\xspace}
%---- BEGIN DOCUMENT
@@ -142,6 +124,10 @@
\label{sec:parameters}
\input{sec/app/parameters.tex}
\section{Reflection Conditions on the Vacuum}
\label{sec:details_reflection}
\input{sec/app/reflection.tex}
%---- BIBLIOGRAPHY
\cleardoubleplainpage{}