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\begin{document}

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\section*{Chiral Algebras}

This entry is about the book

\begin{itemize}%
\item [[Alexander Beilinson]] and [[Vladimir Drinfeld]]

\emph{Chiral Algebras}, Amer. Math. Society 2004

(\href{http://www.ams.org/publications/authors/books/postpub/coll-51}{webpage})

\begin{itemize}%
\item \href{http://www.math.uchicago.edu/~mitya/langlands/chiral/cha_toc.pdf}{Contents}, \href{http://www.math.uchicago.edu/~mitya/langlands/chiral/cha_intro.pdf}{Introduction}, \href{http://www.math.uchicago.edu/~mitya/langlands/chiral/cha_ch1.pdf}{Chapter 1}, \href{http://www.math.uchicago.edu/~mitya/langlands/chiral/cha_ch2.pdf}{Chapter 2}, \href{http://www.math.uchicago.edu/~mitya/langlands/chiral/cha_ch3.pdf}{Chapter 3}, \href{http://www.math.uchicago.edu/~mitya/langlands/chiral/cha_ch4.pdf}{Chapter 4}, \href{http://www.math.uchicago.edu/~mitya/langlands/chiral/cha_ref_new.pdf}{References}, \href{http://www.math.uchicago.edu/~mitya/langlands/chiral/cha_ind.pdf}{Index}

\end{itemize}


\end{itemize}
on [[chiral algebra]]s/[[factorization algebra]]s in the language of [[D-scheme]]s.

\hypertarget{contents}{}\section*{{Contents}}\label{contents}

\noindent\hyperlink{introduction}{Introduction}\dotfill \pageref*{introduction} \linebreak
\noindent\hyperlink{1_axiomatic_patterns}{1. Axiomatic patterns}\dotfill \pageref*{1_axiomatic_patterns} \linebreak
\noindent\hyperlink{2_the_geometry_of_schemes}{2. The Geometry of $\mathcal{D}$-Schemes}\dotfill \pageref*{2_the_geometry_of_schemes} \linebreak
\noindent\hyperlink{21_modules_recollection_and_basics}{2.1 $\mathcal{D}$-modules: recollection and basics}\dotfill \pageref*{21_modules_recollection_and_basics} \linebreak
\noindent\hyperlink{22_the_compound_tensor_structure}{2.2 The compound tensor structure}\dotfill \pageref*{22_the_compound_tensor_structure} \linebreak
\noindent\hyperlink{23_schemes}{2.3 $\mathcal{D}_X$-Schemes}\dotfill \pageref*{23_schemes} \linebreak
\noindent\hyperlink{231_algebras}{2.3.1 $\mathcal{D}_X$-algebras}\dotfill \pageref*{231_algebras} \linebreak
\noindent\hyperlink{232_jet_schemes}{2.3.2 Jet schemes}\dotfill \pageref*{232_jet_schemes} \linebreak
\noindent\hyperlink{2320_the_calculus_of_variations}{2.3.20 The calculus of variations}\dotfill \pageref*{2320_the_calculus_of_variations} \linebreak
\noindent\hyperlink{24_the_space_of_horizontal_sections}{2.4 The space of horizontal sections}\dotfill \pageref*{24_the_space_of_horizontal_sections} \linebreak
\noindent\hyperlink{25_algebras_and_algebroids}{2.5 $Lie^\ast$-algebras and algebroids}\dotfill \pageref*{25_algebras_and_algebroids} \linebreak
\noindent\hyperlink{26_coisson_algebras}{2.6 Coisson algebras}\dotfill \pageref*{26_coisson_algebras} \linebreak
\noindent\hyperlink{27_the_tate_extension}{2.7 The Tate extension}\dotfill \pageref*{27_the_tate_extension} \linebreak
\noindent\hyperlink{28_tate_structures_and_characteristic_classes}{2.8 Tate structures and characteristic classes}\dotfill \pageref*{28_tate_structures_and_characteristic_classes} \linebreak
\noindent\hyperlink{2811}{2.8.11}\dotfill \pageref*{2811} \linebreak
\noindent\hyperlink{29_the_harishchandra_setting_and_the_setting_of_stacks}{2.9 The Harish-Chandra setting and the setting of $c$-stacks}\dotfill \pageref*{29_the_harishchandra_setting_and_the_setting_of_stacks} \linebreak
\noindent\hyperlink{3_local_theory_chiral_basics}{3. Local theory: chiral basics}\dotfill \pageref*{3_local_theory_chiral_basics} \linebreak
\noindent\hyperlink{4_global_theory_chiral_homology}{4. Global theory: chiral homology}\dotfill \pageref*{4_global_theory_chiral_homology} \linebreak
\noindent\hyperlink{related_references}{Related references}\dotfill \pageref*{related_references} \linebreak


\hypertarget{introduction}{}\subsection*{{Introduction}}\label{introduction}

\hypertarget{1_axiomatic_patterns}{}\subsection*{{1. Axiomatic patterns}}\label{1_axiomatic_patterns}

\hypertarget{2_the_geometry_of_schemes}{}\subsection*{{2. The Geometry of $\mathcal{D}$-Schemes}}\label{2_the_geometry_of_schemes}

\hypertarget{21_modules_recollection_and_basics}{}\subsubsection*{{2.1 $\mathcal{D}$-modules: recollection and basics}}\label{21_modules_recollection_and_basics}

\begin{itemize}%
\item [[D-module]]

\end{itemize}
\hypertarget{22_the_compound_tensor_structure}{}\subsubsection*{{2.2 The compound tensor structure}}\label{22_the_compound_tensor_structure}

\hypertarget{23_schemes}{}\subsubsection*{{2.3 $\mathcal{D}_X$-Schemes}}\label{23_schemes}

\begin{itemize}%
\item [[D-scheme]]

\end{itemize}
\hypertarget{231_algebras}{}\paragraph*{{2.3.1 $\mathcal{D}_X$-algebras}}\label{231_algebras}

\hypertarget{232_jet_schemes}{}\paragraph*{{2.3.2 Jet schemes}}\label{232_jet_schemes}

\begin{itemize}%
\item [[jet bundle]]

\end{itemize}
\hypertarget{2320_the_calculus_of_variations}{}\paragraph*{{2.3.20 The calculus of variations}}\label{2320_the_calculus_of_variations}

\begin{itemize}%
\item [[variational calculus]]

\begin{itemize}%
\item [[Lagrangian]]


\item [[action functional]]



\end{itemize}


\end{itemize}
\hypertarget{24_the_space_of_horizontal_sections}{}\subsubsection*{{2.4 The space of horizontal sections}}\label{24_the_space_of_horizontal_sections}

\hypertarget{25_algebras_and_algebroids}{}\subsubsection*{{2.5 $Lie^\ast$-algebras and algebroids}}\label{25_algebras_and_algebroids}

\hypertarget{26_coisson_algebras}{}\subsubsection*{{2.6 Coisson algebras}}\label{26_coisson_algebras}

\begin{itemize}%
\item [[Coisson algebra]]s

\end{itemize}
\hypertarget{27_the_tate_extension}{}\subsubsection*{{2.7 The Tate extension}}\label{27_the_tate_extension}

\hypertarget{28_tate_structures_and_characteristic_classes}{}\subsubsection*{{2.8 Tate structures and characteristic classes}}\label{28_tate_structures_and_characteristic_classes}

\hypertarget{2811}{}\paragraph*{{2.8.11}}\label{2811}

\begin{itemize}%
\item [[vertical differential form]]


\item [[variational bicomplex]]



\end{itemize}
\hypertarget{29_the_harishchandra_setting_and_the_setting_of_stacks}{}\subsubsection*{{2.9 The Harish-Chandra setting and the setting of $c$-stacks}}\label{29_the_harishchandra_setting_and_the_setting_of_stacks}

\hypertarget{3_local_theory_chiral_basics}{}\subsection*{{3. Local theory: chiral basics}}\label{3_local_theory_chiral_basics}

\hypertarget{4_global_theory_chiral_homology}{}\subsection*{{4. Global theory: chiral homology}}\label{4_global_theory_chiral_homology}

\hypertarget{related_references}{}\subsection*{{Related references}}\label{related_references}

Much complementary content by the same authors is also in the developing book on the geometric Langlands program

\begin{itemize}%
\item [[Alexander Beilinson]], [[Vladimir Drinfeld]], \emph{Quantization of the Hitchin system and Hecke eigensheaves}, draft, \href{http://www.math.uchicago.edu/~mitya/langlands/hitchin/BD-hitchin.pdf}{pdf}

\end{itemize}
A goood accessible survey of or introduction into some of the developments in this book can be found around section 8.3

\begin{itemize}%
\item [[Frédéric Paugam]], \emph{Towards the mathematics of quantum field theory} (\href{http://www.math.jussieu.fr/~fpaugam/documents/enseignement/master-mathematical-physics-impa-v01-2011.pdf}{pdf})

\end{itemize}
and section 3 of

\begin{itemize}%
\item [[Frédéric Paugam]], \emph{Histories and observables in covariant field theory} Journal of Geometry and Physics (2010) (\href{http://arxiv.org/abs/1010.3210}{arXiv})

\end{itemize}
with more details in

\begin{itemize}%
\item [[Frédéric Paugam]], \emph{Homotopical Poisson Reduction of gauge theories} (\href{http://people.math.jussieu.fr/~fpaugam/documents/homotopical-poisson-reduction-of-gauge-theories.pdf}{pdf})

\end{itemize}
In the context of [[factorization algebra of observables]]:

\begin{itemize}%
\item [[Kevin Costello]], [[Owen Gwilliam]], \emph{[[Factorization algebras in perturbative quantum field theory]]}

\end{itemize}
category: reference



\end{document}