% !TeX spellcheck = en_US
% !TeX encoding = UTF-8
\documentclass[a4paper]{article}
\usepackage{fullpage}
\usepackage{tikz}
\usepackage[shortcuts]{extdash}

\begin{document}

\centerline{\Large Introduction into integrable quantum field theories}
\bigskip
\leftline{\bf Abstract}
\medskip
The lecture course is dedicated to two-dimensional integrable field theories, including the following topics: conformal field theory, massive integrable models, bootstrap methods.



\begin{enumerate}
\parsep=0pt \itemsep=0pt

\item Free field theories

\begin{enumerate}
\item Massless free boson on the cylinder and on the plane

{\it Massless free boson on the cylinder. Conformal map to the plane. Wick's theorem and exponential operators. Energy\-/momentum tensor and Virasoro algebra.}

\item Massless free fermion on the cylinder and on the plane

{\it Massless free Majorana fermion on the cylinder. Neveu\--Schwarz and Ramond boundary conditions. Conformal map to the plane. Order and disorder operators. Energy-momentum tensor and Virasoro algebra.}

\item Massive free fields.

{\it Massive fields. Nonequivalence of radial and plane quantizations. Energy\-/momentum conservation law.}

\end{enumerate}

\item Conformal field theory

\begin{enumerate}

\item Energy\-/momentum tensor and Virasoro algebra.

{\it Operator product expansion for the energy\-/momentum tensor. Primary and descendant operators. Virasoro algebra and its representations. Null vectors and degenerate modules.}

\item Conformal blocks and crossing symmetry

{\it Operator product expansion of two primary operators. Fusion rules. Structure constants and conformal families. Four-point correlation functions and conformal blocks. Minimal conformal models.}

\item Free boson representation.

{\it Charge at infinity and modified energy\-/momentum tensor. Representation of primary fields with exponential operators. Representation for conformal blocks and correlation functions.}

\end{enumerate}

\item Boson-fermion correspondence

\begin{enumerate}

\item $O(2)$ model and sine-Gordon model.

{\it Vortices in the $O(2)$ model and their description in terms of the dual field. Action of vortices. Condensation of vortices and Berezinsky\--Kosterlitz\--Thouless transition. Relation to the sine-Gordon model.}

\item Thirring model and its bosonization.

{\it Massive and massless Thirring models. Bosonization of the massless model. Massive term as a cosine perturbation.}

\item Bethe Ansatz for the Thirring model.

{\it Pseudovacuum in the Thirring model. Pseudoparticles and their scattering. Construction of the true vacuum. Hole and its mass.}

\end{enumerate}

\item Exact $S$-matrices

\begin{enumerate}

\item Perturbation theory in the Thirring model.

{\it Two-particle scattering in the Thirring model. Cancellation of the multiple production amplitudes. The role of integrals of motion.}

\item Exact $S$ matrices and Yang\--/Baxter equation.

{\it Factorized scattering and the Yang\--/Baxter equation. Crossing symmetry and unitarity. A solution to the Yang\--/Baxter equation. Its connection to the Thirring and sine\-Gordon theory.}

\item Questions, discussion and examination.

\end{enumerate}

\end{enumerate}


\end{document}
