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diff --git a/Figs/beta_phase.pdf b/Figs/beta_phase.pdf
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diff --git a/Figs/hierarchical_boxes.pdf b/Figs/hierarchical_boxes.pdf
new file mode 100644
index 0000000..5eb4dec
--- /dev/null
+++ b/Figs/hierarchical_boxes.pdf
diff --git a/Figs/hierarchical_boxtree.pdf b/Figs/hierarchical_boxtree.pdf
new file mode 100644
index 0000000..28b238f
--- /dev/null
+++ b/Figs/hierarchical_boxtree.pdf
diff --git a/Figs/kondo_model.pdf b/Figs/kondo_model.pdf
new file mode 100644
index 0000000..589cf74
--- /dev/null
+++ b/Figs/kondo_model.pdf
diff --git a/Figs/susc_plot_temp.pdf b/Figs/susc_plot_temp.pdf
new file mode 100644
index 0000000..1e8f863
--- /dev/null
+++ b/Figs/susc_plot_temp.pdf
diff --git a/Jauslin_Como_2015.tex b/Jauslin_Como_2015.tex
new file mode 100644
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--- /dev/null
+++ b/Jauslin_Como_2015.tex
@@ -0,0 +1,324 @@
+\documentclass{kiss}
+\usepackage{presentation}
+\usepackage{header}
+
+\begin{document}
+\pagestyle{empty}
+\hbox{}\vfil
+\bf
+\large
+\hfil Non-perturbative renormalization group\par
+\smallskip
+\hfil in a hierarchical Kondo model\par
+\vfil
+\hfil Ian Jauslin
+\rm
+\normalsize
+
+\vfil
+\small
+\hfil joint with {\normalsize\bf G.~Benfatto} and {\normalsize\bf G.~Gallavotti}\par
+\vskip10pt
+arXiv: {\tt1506.04381}\hfill{\tt http://ian.jauslin.org/}
+\eject
+
+\pagestyle{plain}
+\setcounter{page}{1}
+
+\title{Kondo model}
+\begin{itemize}
+\item s-d model: [P.~Anderson, 1960] [J.~Kondo, 1964]:
+\itemptchange{$\scriptstyle\blacktriangleright$ }
+\begin{itemize}
+\item 1D chain of non-interacting spin-1/2 fermions: {\it electrons}.
+\item lone spin-1/2 fermion: {\it impurity}.
+\item the impurity interacts with the electron at 0.
+\end{itemize}
+\itemptreset
+\end{itemize}
+\vskip0ptplus3fil
+\hfil\includegraphics[width=0.8\textwidth]{Figs/kondo_model.pdf}\par
+\vskip0ptplus3fil
+\eject
+
+\title{Kondo Hamiltonian}
+\vskip5pt
+\hfil\includegraphics[width=0.8\textwidth]{Figs/kondo_model.pdf}\par
+$$
+H=H_0+V
+$$
+\begin{itemize}
+\item $H_0$: kinetic term of the {\it electrons}
+$$
+H_0:=\sum_{x}\sum_{\alpha=\uparrow,\downarrow}c^\dagger_\alpha(x)\,\left(-\frac{\Delta}2-1\right)\,c_\alpha(x)
+$$
+\itemptchange{$\scriptstyle\blacktriangleright$ }
+\begin{itemize}
+\item $c_\alpha(x)$: fermionic annihilation operator
+\item $\alpha$: spin
+\item $x$: site
+\end{itemize}
+\itemptreset
+\end{itemize}
+\eject
+
+
+\title{Kondo Hamiltonian}
+\vskip5pt
+\hfil\includegraphics[width=0.8\textwidth]{Figs/kondo_model.pdf}\par
+$$
+H=H_0+V
+$$
+\begin{itemize}
+\item $V$: interaction with the {\it impurity}
+$$
+V=-\lambda_0\sum_{j=1,2,3}\sum_{\alpha_1,\alpha_2,\alpha_3,\alpha_4}c^\dagger_{\alpha_1}(0)\sigma^j_{\alpha_1,\alpha_2}c_{\alpha_2}(0)\, d^\dagger_{\alpha_3}\sigma^j_{\alpha_3,\alpha_4}d_{\alpha_4}
+$$
+\itemptchange{$\scriptstyle\blacktriangleright$ }
+\begin{itemize}
+\item $d_\alpha$: fermionic annihilation operator
+\item $\sigma^j$: Pauli matrix
+\item $\lambda_0>0$: {\it ferromagnetic} case
+\item $\lambda_0<0$: {\it anti-ferromagnetic} case \end{itemize}
+\itemptreset
+\end{itemize}
+\eject
+
+\title{Kondo effect: magnetic susceptibility}
+\begin{itemize}
+\item Magnetic susceptibility: response to a magnetic field $h$:
+$$
+\chi(h,\beta):=\partial_hm(h,\beta).
+$$
+($m(h,\beta)$: magnetization).
+\item Isolated impurity:
+$$
+\chi^{(0)}(0,\beta)=\frac\beta2\mathop{\longrightarrow}_{\beta\to\infty}\infty
+$$
+\item Chain of electrons: Pauli paramagnetism:
+$$
+\lim_{\beta\to\infty}\lim_{L\to\infty}\frac1L\chi_e(0,\beta)<\infty.
+$$
+\end{itemize}
+\eject
+
+\title{Kondo effect: magnetic susceptibility}
+\begin{itemize}
+\item Turn on the interaction: $\lambda_0\neq0$. Impurity susceptibility $\chi^{(\lambda_0)}(h,\beta)$.
+\item Ferromagnetic interaction ($\lambda_0>0$):
+$$
+\lim_{\beta\to\infty}\chi^{(\lambda_0)}(0,\beta)=\infty.
+$$
+\item Anti-ferromagnetic interaction ($\lambda_0>0$):
+$$
+\lim_{\beta\to\infty}\chi^{(\lambda_0)}(0,\beta)<\infty.
+$$
+\item {\it Non-perturbative} effect: the qualitative behavior changes as soon as $\lambda_0\neq0$.
+\end{itemize}
+\eject
+
+\title{Previous results}
+\begin{itemize}
+\item [J.~Kondo, 1964]: third order Born approximation.
+\vskip0pt plus3fil
+\item [P.~Anderson, 1970], [K.~Wilson, 1975]: renormalization group approach
+\itemptchange{$\scriptstyle\blacktriangleright$ }
+\begin{itemize}
+\item Sequence of effective Hamiltonians at varying energy scales.
+\item For anti-ferromagnetic interactions, the effective Hamiltonians go to a {\it non-trivial fixed point}.
+\item Anderson: instability of the trivial fixed point ($H_0$).
+\item Wilson: numerical diagonalization at each step, and perturbative expansions around the trivial and non-trivial fixed points.
+\end{itemize}
+\end{itemize}
+\eject
+
+\title{Current results}
+\begin{itemize}
+\item Hierarchical Kondo model: idealization of the Kondo model that has the same scaling properties.
+\item It is {\it exactly solvable}: the map relating the effective theories at different scales is {\it explicit} (no perturbative expansions).
+\item With $\lambda_0<0$, the flow tends to a non-trivial fixed point, and $\chi^{(\lambda_0)}<\infty$ in the $\beta\to\infty$ limit (Kondo effect).
+\item{\tt Remark}: [Andrei, 1980]: the Kondo model (suitably linearized) is exactly solvable via Bethe Ansatz.
+\end{itemize}
+\eject
+
+\title{Field theory for the Kondo model}
+\begin{itemize}
+\item Partition function $Z:=\mathrm{Tr}(e^{-\beta H})$.
+\vskip5pt
+\item By introducing an extra dimension ({\it imaginary time}), $Z$ can be expressed as the {\it Gaussian} average over a {\it Grassmann} algebra:
+$$
+Z=\left<e^{-\int_0^\beta dt\ \mathcal V(t)}\right>
+$$
+where
+$$
+\mathcal V(t)=-\lambda_0\kern-10pt\sum_{\displaystyle\mathop{\scriptstyle j=1,2,3}_{\alpha_1,\alpha_2,\alpha_3,\alpha_4}}\kern-10pt
+\psi^+_{\alpha_1}(0,t)\sigma^j_{\alpha_1,\alpha_2}\psi^-_{\alpha_2}(0,t)\, \varphi^+_{\alpha_3}(t)\sigma^j_{\alpha_3,\alpha_4}\varphi^-_{\alpha_4}(t)
+$$
+with $\{\psi^\pm_\alpha(0,t),\psi^\pm_{\alpha'}(0,t')\}=0$, $\{\varphi^\pm_\alpha(t),\varphi^\pm_{\alpha'}(t')\}=0$.
+\end{itemize}
+\eject
+
+\title{Hierarchical fields}
+\hfil\includegraphics[width=0.8\textwidth]{Figs/hierarchical_boxes.pdf}\par
+\begin{itemize}
+\item For each $m<0$, we introduce fields {\it on scale $m$} indexed by an interval:
+$$
+\psi_\alpha^\pm(\Delta_{i,\pm}^{[m]}),\quad
+\varphi_\alpha^\pm(\Delta_{i,\pm}^{[m]})
+$$
+where
+$$\begin{array}l
+\Delta_{i,-}^{[m]}:=[2^{-m}i,2^{-m}(i+\frac12))\\[0.3cm]
+\Delta_{i,+}^{[m]}:=[2^{-m}(i+\frac12),2^{-m}(i+1))
+\end{array}$$
+\item There are 8 fields in each $\Delta_{i,\pm}^{[m]}$.
+\end{itemize}
+\eject
+
+\title{Hierarchical fields}
+\begin{itemize}
+\item Split fields over scales:
+$$
+\psi_\alpha^\pm(t):=\sum_{m}\psi_\alpha^{[m]\pm}(\Delta^{[m]}(t)),\quad
+\varphi_\alpha^\pm(t):=\sum_{m}\varphi_\alpha^{[m]\pm}(\Delta^{[m]}(t))
+$$
+\end{itemize}
+\hfil\includegraphics[width=0.8\textwidth]{Figs/hierarchical_boxtree.pdf}\par
+\vfil
+\eject
+
+\title{Hierarchical propagators}
+\begin{itemize}
+\item Moments:
+$$\begin{array}{r@{\ }l}
+\left<\psi_\alpha^{[m]-}(\Delta_{i,-\eta}^{[m]})\psi_\alpha^{[m]+}(\Delta_{i,\eta}^{[m]})\right>=&\eta 2^m\\[0.3cm]
+\left<\varphi_\alpha^{[m]-}(\Delta_{i,-\eta}^{[m]})\varphi_\alpha^{[m]+}(\Delta_{i,\eta}^{[m]})\right>=&\eta
+\end{array}$$
+\item Full propagator:
+$$
+\left<\psi_\alpha^{-}(t)\psi_\alpha^{+}(t')\right>=\mathrm{sign}(t-t') 2^{m_{t,t'}},\quad
+\left<\varphi_\alpha^{-}(t)\varphi_\alpha^{+}(t')\right>=\mathrm{sign}(t-t')
+$$
+\item For the (non-hierarchical) Kondo model:
+$$\begin{array}{r@{\ }l}
+\left<\psi_\alpha^{-}(0,t)\psi_\alpha^{+}(0,t')\right>\approx&\sum_m 2^{m}g_\psi^{[0]}(2^m(t-t')),\\[0.3cm]
+\left<\varphi_\alpha^{-}(t)\varphi_\alpha^{+}(t')\right>\approx&\sum_m g^{[0]}_\varphi(2^m(t-t'))
+\end{array}$$
+\end{itemize}
+\eject
+
+\title{Hierarchical beta function}
+\begin{itemize}
+\item Compute $Z$ by $\mathcal V^{[0]}(t):=\mathcal V(t)$
+$$
+e^{-\int dt\ \mathcal V^{[m-1]}(t)}:=\left<e^{-\int dt\ \mathcal V^{[m]}(t)}\right>_m
+$$
+
+\item Effective potential:
+$$
+\int dt\ \mathcal V^{[m]}(t)=\sum_{i=1}^{2^{-m}}\mathcal V^{[m]}_{i,-}+\mathcal V^{[m]}_{i,+}
+$$
+\item Iteration
+$$
+\left<e^{-\int dt\ \mathcal V^{[m]}(t)}\right>_m=\prod_{i=1}^{2^{-m}}\left<e^{-(\mathcal V^{[m]}_{i,-}+\mathcal V_{i,+}^{[m]})}\right>_m
+$$
+\item By anti-commutation of the fields, $e^{-\mathcal V_{i,\pm}^{[m]}}$ is a polynomial in the fields of order $\leqslant 8$.
+\end{itemize}
+\eject
+
+\title{Hierarchical beta function}
+\begin{itemize}
+\item The computation of the beta function reduces to computing the average of a degree-$16$ polynomial.
+\item 4 running coupling constants $\ell_0,\cdots,\ell_3$:
+$$
+e^{-\int dt\ \mathcal V^{[m]}(t)}
+=\sum_{i,\eta}\sum_{n=0}^3\ell_n^{[m]}O_{n}^{[\leqslant m]}(\Delta_{i,\eta})
+$$
+\end{itemize}
+\eject
+
+\title{Hierarchical beta function}
+\begin{itemize}
+\item Beta function ({\it exact})
+$$\begin{array}{r@{\ }l}
+C^{[m]}=&\displaystyle1+ 3\ell_0^2+9\ell_1^2+9\ell_2^2+324\ell_3^2\\[0.3cm]
+\ell_0^{[m-1]}=&\displaystyle\frac1C\Big(\ell_0 +18\ell_0\ell_3+3 \ell_0\ell_2+3 \ell_0\ell_1 -2\ell_0^2\Big)\\[0.5cm]
+\ell_1^{[m-1]}=&\displaystyle\frac1C\Big( \frac12\ell_1+9\ell_2\ell_3 +\frac14\ell_0^2\Big)\\[0.5cm]
+\ell_2^{[m-1]}=&\displaystyle\frac1C\Big(2\ell_2+36\ell_1\ell_3+ \ell_0^2\Big)\\[0.5cm]
+\ell_3^{[m-1]}=&\displaystyle\frac1C\Big(\frac12\ell_3+\frac14\ell_1\ell_2+\frac1{24} \ell_0^2\Big).
+\end{array}$$
+\end{itemize}
+\eject
+
+\title{Hierarchical beta function}
+\begin{itemize}
+\item Beta function ({\it exact})
+$$\begin{array}{r@{\ }l}
+C^{[m]}=&\displaystyle1+ 3\ell_0^2+9\ell_1^2+9\ell_2^2+324\ell_3^2\\[0.3cm]
+\color{blue}\ell_0^{[m-1]}=&\color{blue}\displaystyle\frac1C\Big(\ell_0 +18\ell_0\ell_3+3 \ell_0\ell_2+3 \ell_0\ell_1 -2\ell_0^2\Big)\\[0.5cm]
+\color{darkgreen}\ell_1^{[m-1]}=&\color{darkgreen}\displaystyle\frac1C\Big( \frac12\ell_1+9\ell_2\ell_3 +\frac14\ell_0^2\Big)\\[0.5cm]
+\color{red}\ell_2^{[m-1]}=&\color{red}\displaystyle\frac1C\Big(2\ell_2+36\ell_1\ell_3+ \ell_0^2\Big)\\[0.5cm]
+\color{darkgreen}\ell_3^{[m-1]}=&\color{darkgreen}\displaystyle\frac1C\Big(\frac12\ell_3+\frac14\ell_1\ell_2+\frac1{24} \ell_0^2\Big).
+\end{array}$$
+{\color{red}relevant}, {\color{blue}marginal}, {\color{darkgreen}irrelevant}
+\end{itemize}
+\eject
+
+\title{Flow}
+\vfil
+\hfil\includegraphics[width=0.8\textwidth]{Figs/beta_phase.pdf}\par
+Fixed points: $\bm\ell^{(0)}$, $\bm\ell^{(+)}$, $\bm\ell^*$, $\bm\ell^{(-)}$.
+\eject
+
+\title{Fixed points}
+\begin{itemize}
+\item $\bm\ell^{(0)}$: unstable.
+\item $\bm\ell^{(+)}$: ferromagnetic ($\lambda_0>0$).
+\item $\bm\ell^*$: anti-ferromagnetic ($\lambda_0<0$).
+\end{itemize}
+\eject
+
+\title{Susceptibility}
+\begin{itemize}
+\item Add magnetic field $h$ on the impurity.
+\item New term in the potential:
+$$
+-h \sum_{j\in\{1,2,3\}}\bm\omega_j \int dt\sum_{\alpha,\alpha'}\varphi^+_{\alpha}(t)\sigma^j_{\alpha,\alpha'} \varphi^-_{\alpha'}(t).
+$$
+\item 9 running coupling constants.
+\item The susceptibility can be computed by deriving $C^{[m]}$ with respect to $h$.
+\end{itemize}
+\eject
+
+\title{Kondo effect}
+\begin{itemize}
+\item Fix $h=0$.
+\item At $\bm\ell^{(+)}$, the susceptibility diverges as $\beta$.
+\item At $\bm\ell^*$, the susceptibility remains finite in the $\beta\to\infty$ limit.
+\end{itemize}
+\hfil\includegraphics[width=150pt]{Figs/susc_plot_temp.pdf}\par
+\eject
+
+\title{Open questions}
+\begin{itemize}
+\item Magnetic field on the chain as well. This requires defining the hierarchical model to reflect the $x$-dependence of $\psi(x,t)$.
+\item Rigorous renormalization group analysis for the Kondo model (non-hierarchical).
+\item The exact solvability of the hierarchical Kondo model is merely a consequence of the fermionic nature of the system. Other fermionic hierarchical models can be studied to investigate other non-perturbative phenomena, e.g. high-$T_c$ superconductivity.
+\end{itemize}
+\eject
+
+\title{Epilogue: {\tt meankondo}}
+\begin{itemize}
+\item The computation in the $h$-dependent case requires computing 100 Feynman diagrams.
+\item By adding the field on the entire chain (open problem), this number increases to 1089.
+\item Software to perform the computation: {\tt meankondo}.
+\item {\tt meankondo} can be configured to study any fermionic hierarchical model.
+\end{itemize}
+\hfil{\tt http://ian.jauslin.org/software/meankondo/}
+
+\end{document}
+
+
+
+
+
diff --git a/README b/README
new file mode 100644
index 0000000..f84bb0a
--- /dev/null
+++ b/README
@@ -0,0 +1,32 @@
+* Typeset
+
+In order to typeset the LaTeX presentation, run
+  pdflatex Jauslin_Como_2015.tex
+  pdflatex Jauslin_Como_2015.tex
+
+
+* Files
+
+  Jauslin_Como_2015.tex
+    body of the presentation.
+
+  Figs :
+    figures.
+
+  header.sty :
+    packages and local definitions
+
+  presentation.sty :
+    presentation style file.
+
+  kiss.cls :
+    barebones class file
+
+
+* Comment on the presentation style
+
+This presentation is typeset using the 'presentation.sty' style file, in which
+the margins and sizes are set to make the output look like a presentation, and
+several useful commands are defined.
+
+The LaTeX 'beamer' package is not used.
diff --git a/header.sty b/header.sty
new file mode 100644
index 0000000..333385b
--- /dev/null
+++ b/header.sty
@@ -0,0 +1,17 @@
+%%
+%% Packages and local definitions
+%%
+
+%% load packages
+% colors
+\usepackage{color}
+% include figures
+\usepackage{graphicx}
+% extra symbols and fonts
+\usepackage{amsfonts}
+\usepackage{amssymb}
+\usepackage{dsfont}
+\usepackage{bm}
+
+%% dark green color
+\definecolor{darkgreen}{RGB}{0,128,0}
diff --git a/kiss.cls b/kiss.cls
new file mode 100644
index 0000000..dc1bdbc
--- /dev/null
+++ b/kiss.cls
@@ -0,0 +1,42 @@
+%%
+%% Barebones class declaration
+%%
+
+\NeedsTeXFormat{LaTeX2e}[1995/12/01]
+\ProvidesClass{kiss}
+
+\setlength\paperheight {297mm}
+\setlength\paperwidth  {210mm}
+
+%% fonts
+\input{size11.clo}
+\DeclareOldFontCommand{\rm}{\normalfont\rmfamily}{\mathrm}
+\DeclareOldFontCommand{\sf}{\normalfont\sffamily}{\mathsf}
+\DeclareOldFontCommand{\tt}{\normalfont\ttfamily}{\mathtt}
+\DeclareOldFontCommand{\bf}{\normalfont\bfseries}{\mathbf}
+\DeclareOldFontCommand{\it}{\normalfont\itshape}{\mathit}
+\DeclareOldFontCommand{\sl}{\normalfont\slshape}{\@nomath\sl}
+\DeclareOldFontCommand{\sc}{\normalfont\scshape}{\@nomath\sc}
+
+%% something is wrong with \thepage, redefine it
+\gdef\thepage{\the\c@page}
+
+%% default offsets: 1in, correct with \hoffset and \voffset
+%\hoffset=0pt
+%\voffset=0pt
+%% horizontal margins
+%\oddsidemargin=31pt
+%\evensidemargin=31pt
+%% vertical margin
+%\topmargin=20pt
+%% body size
+%\textwidth=390pt
+%\textheight=592pt
+%% header size and margin
+%\headheight=12pt
+%\headsep=25pt
+%% footer size
+%\footskip=30pt
+%% margin size and margin
+%\marginparwidth=35pt
+%\marginparsep=10pt
diff --git a/presentation.sty b/presentation.sty
new file mode 100644
index 0000000..e55928f
--- /dev/null
+++ b/presentation.sty
@@ -0,0 +1,110 @@
+%%
+%% Presentation style
+%%
+
+%% can call commands even when they are not defined
+\def\safe#1{%
+\ifdefined#1%
+#1%
+\else%
+{\color{red}\bf?}%
+\fi%
+}
+
+
+%% paper size
+\setlength\paperheight{240pt}
+\setlength\paperwidth{320pt}
+
+%% body size
+% height=paperheight-2xtopmargin-footskip
+\textheight=208pt
+% width=paperwidth-2xoddsidemargin
+\textwidth=272pt
+
+%% margins
+\voffset=-1in
+\hoffset=-1in
+\oddsidemargin=24pt
+\evensidemargin=24pt
+\topmargin=8pt
+\headheight=0pt
+\headsep=0pt
+\marginparsep=0pt
+\marginparwidth=0pt
+\footskip=16pt
+\skip\footins=0pt
+
+%% reset skips
+\parskip=0pt
+\parindent=0pt
+\baselineskip=0pt
+\AtBeginDocument{
+}
+
+%% footer
+\def\ps@plain{
+  \def\@oddhead{}
+  \def\@evenhead{\@oddhead}
+  \def\@oddfoot{\tiny\hfill\thepage/\safe\slidecount\hfill}
+  \def\@evenfoot{\@oddfoot}
+}
+\def\ps@empty{
+  \def\@oddhead{}
+  \def\@evenhead{\@oddhead}
+  \def\@oddfoot{}
+  \def\@evenfoot{\@oddfoot}
+}
+
+%% save total slide count
+\AtEndDocument{
+  \immediate\write\@auxout{\noexpand\gdef\noexpand\slidecount{\thepage}}
+}
+
+\pagestyle{plain}
+
+%% title of slide
+\def\title#1{
+  \hfil{\bf\large #1}\par
+  \hfil\vrule width0.75\textwidth height0.3pt\par
+  \vskip5pt
+}
+
+%% itemize
+\newlength\itemizeskip
+% left margin for items
+\setlength\itemizeskip{20pt}
+% item symbol
+\def\itemizept{\textbullet}
+\newlength\itemizeseparator
+% space between the item symbol and the text
+\setlength\itemizeseparator{5pt}
+
+\newlength\current@itemizeskip
+\setlength\current@itemizeskip{0pt}
+\def\itemize{
+  \vfil
+  \addtolength\current@itemizeskip{\itemizeskip}
+  \leftskip\current@itemizeskip
+}
+\def\enditemize{
+  \addtolength\current@itemizeskip{-\itemizeskip}
+  \par\leftskip\current@itemizeskip
+  \vfil
+}
+\newlength\itempt@total
+\def\item{
+  \settowidth\itempt@total{\itemizept}
+  \addtolength\itempt@total{\itemizeseparator}
+  \par
+  \vfil
+  \hskip-\itempt@total\itemizept\hskip\itemizeseparator
+}
+
+\def\itemptchange#1{
+  \let\itempt@prev\itemizept
+  \def\itemizept{#1}
+}
+\def\itemptreset{
+  \def\itemizept{\itempt@prev}
+}
diff --git a/symbols.sty b/symbols.sty
new file mode 100644
index 0000000..84ae838
--- /dev/null
+++ b/symbols.sty
@@ -0,0 +1,61 @@
+%%
+%% symbols
+%%
+
+\def\deriv#1#2{\frac{d#1}{d#2}}
+\def\pard#1#2{\frac{\partial #1}{\partial #2}}
+\def\mAthop#1{\mathop{\scriptstyle#1}}
+
+\def\rp{\right)}
+\def\lp{\left(}
+\let\(\lp
+\let\)\rp
+
+\def\ma{\\[0.2cm]}
+\def\n{\\[0.5cm]}
+\def\N{\\[1cm]}
+
+\let\mc\mathcal
+\let\mbb\mathbb
+\let\mf\mathfrak
+\let\mds\mathds
+\let\mrm\mathrm
+\let\mbf\mathbf
+
+\def\R{\mathbb{R}}
+\def\C{\mathbb{C}}
+\def\tr{\mathrm{Tr}}
+\let\lra\longrightarrow
+\def\+{^\dagger}
+\let\ge\geqslant
+\let\le\leqslant
+
+\def\ket#1{\left|#1\right>}
+\def\bra#1{\left<#1\right|}
+\def\<{\left<}
+\def\>{\right>}
+
+\def\Par{\par\penalty10000}
+\def\Smallskip{\smallskip\penalty10000}
+\def\Medskip{\medskip\penalty10000}
+\def\Bigskip{\bigskip\penalty10000}
+
+\def\vvect#1{\lp\begin{array}{c}#1\end{array}\rp}
+\def\hvect#1#2{\lp\begin{array}{*{#1}{c}}#2\end{array}\rp}
+\def\mat#1#2{\lp\begin{array}{*{#1}{c}}#2\end{array}\rp}
+\long\def\sys#1{\left\{\begin{array}l#1\end{array}\right.}
+
+\def\sint{\int\kern-3pt}
+\def\sintb#1#2{\int_{#1}^{#2}\kern-.3cm}
+\def\sIntb#1#2{\displaystyle\int_{#1}^{#2}\kern-.3cm}
+\def\soint{\oint\kern-3pt}
+\def\sOint{\displaystyle\oint\kern-3pt}
+
+\def\po{$\bullet$ }
+\def\as{$\ast$ }
+\def\spo{$\scriptstyle\blacktriangleright$ }
+
+\def\qed{\hfill$\square$}
+
+\def\itemsymbolt{\spo}
+