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\begin{document}

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\section*{scattering amplitude}

\hypertarget{context}{}\subsubsection*{{Context}}\label{context}

\hypertarget{algebraic_quantum_field_theory}{}\paragraph*{{Algebraic Quantum Field Theory}}\label{algebraic_quantum_field_theory}

[[!include AQFT and operator algebra contents]]

\hypertarget{physics}{}\paragraph*{{Physics}}\label{physics}

[[!include physicscontents]]

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

\noindent\hyperlink{idea}{Idea}\dotfill \pageref*{idea} \linebreak
\noindent\hyperlink{examples}{Examples}\dotfill \pageref*{examples} \linebreak
\noindent\hyperlink{in_chernsimons_theory}{In Chern-Simons theory}\dotfill \pageref*{in_chernsimons_theory} \linebreak
\noindent\hyperlink{of_monopoles}{Of monopoles}\dotfill \pageref*{of_monopoles} \linebreak
\noindent\hyperlink{related_concepts}{Related concepts}\dotfill \pageref*{related_concepts} \linebreak
\noindent\hyperlink{references}{References}\dotfill \pageref*{references} \linebreak
\noindent\hyperlink{general}{General}\dotfill \pageref*{general} \linebreak
\noindent\hyperlink{analytic_methods}{Analytic methods}\dotfill \pageref*{analytic_methods} \linebreak
\noindent\hyperlink{in_super_yangmills_theory}{In super Yang-Mills theory}\dotfill \pageref*{in_super_yangmills_theory} \linebreak
\noindent\hyperlink{in_string_theory_and_higher_supergravity}{In string theory and higher supergravity}\dotfill \pageref*{in_string_theory_and_higher_supergravity} \linebreak
\noindent\hyperlink{motivic_structure}{Motivic structure}\dotfill \pageref*{motivic_structure} \linebreak


\hypertarget{idea}{}\subsection*{{Idea}}\label{idea}

In [[quantum field theory]] scattering amplitudes are the [[probability amplitudes]] for processes of [[scattering]] of [[fundamental particles]] (or [[fundamental strings]] etc.) off each other. The collection of scattering amplitudes forms the \emph{[[S-matrix]]}. In [[perturbative quantum field theory]] its contributions may be labeled by [[Feynman diagrams]], whence it is also called the \emph{[[Feynman perturbation series]]}.

Of particular interest are [[vacuum amplitudes]] which are scattering amplitudes ``where nothing external scatters'' hence for no incoming and no outgoing states. The [[1-loop]] vacuum amplitudes are [[regularization (physics)|regularized]] [[traces]] over [[Feynman propagators]]. These are the incarnations of [[zeta functions]], [[L-functions]] and [[eta functions]] in [[physics]].

\hypertarget{examples}{}\subsection*{{Examples}}\label{examples}

\hypertarget{in_chernsimons_theory}{}\subsubsection*{{In Chern-Simons theory}}\label{in_chernsimons_theory}

The Feynman amplitudes of [[higher Chern-Simons theory]], such as [[AKSZ sigma-models]], regarded in their incarnation as [[Feynman amplitudes on compactified configuration spaces of points]], serve to exhibit a [[graph complex]]-model for the [[de Rham complex]] of [[Fulton-MacPherson compactifications]] of [[configuration spaces of points]] by the construction recalled \href{Fulton-MacPherson+operad#RelationToGraphComplexes}{there}. See the pointers at \emph{[[Chern-Simons theory]]} \href{Chern-Simons+theory#FeynmanPerturbationSeries}{here}.

\hypertarget{of_monopoles}{}\subsubsection*{{Of monopoles}}\label{of_monopoles}

See at \emph{[[moduli space of monopoles]]} the section \emph{\href{moduli+space+of+monopoles#ScatteringAmplitudesofMonopoles}{Scattering amplitudes of monopoles}}.

\hypertarget{related_concepts}{}\subsection*{{Related concepts}}\label{related_concepts}

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


\item [[scattering matrix]]


\item [[scattering cross section]]


\item [[perturbative quantum field theory]]


\item [[n-point function]], [[correlator]]


\item [[Feynman diagram]]


\item [[abstract scattering theory]]


\item [[cluster decomposition]]


\item [[renormalization]]


\item [[on-shell recursion]], [[planar limit]]


\item [[form factor (QFT)]]


\item [[KLT relations]]


\item [[amplituhedron]]


\item [[string theory results applied elsewhere]]


\item [[string scattering amplitude]]


\item [[motives in physics]]


\item [[graph complex]], [[formality of the little n-disk operad]]



\end{itemize}
\hypertarget{references}{}\subsection*{{References}}\label{references}

\hypertarget{general}{}\subsubsection*{{General}}\label{general}

\begin{itemize}%
\item Henriette Elvang, Yu-tin Huang, \emph{Scattering Amplitudes} (\href{http://arxiv.org/abs/1308.1697}{arXiv:1308.1697})

\end{itemize}
intended to

\begin{quote}%
bridge the gap between a standard course in quantum field theory and recent fascinating developments in the studies of on-shell scattering amplitudes.


\end{quote}
\begin{itemize}%
\item Tomasz R. Taylor, \emph{A Course in Amplitudes} (\href{https://arxiv.org/abs/1703.05670}{arXiv:1703.05670})


\item Stephen J. Summers, [[Detlev Buchholz]], \emph{Scattering in Relativistic Quantum Field Theory: Fundamental Concepts and Tools} (\href{https://arxiv.org/abs/math-ph/0509047}{arXiv:math-ph/0509047})


\item Clifford Cheung, \emph{TASI Lectures on Scattering Amplitudes} (\href{https://arxiv.org/abs/1708.03872}{arXiv:1708.03872})



\end{itemize}
A historical overview of the development of on-shell methods/analytic methods is in

\begin{itemize}%
\item [[Lance Dixon]], \emph{Calculating Amplitudes}, December 2013 (\href{http://www.preposterousuniverse.com/blog/2013/10/03/guest-post-lance-dixon-on-calculating-amplitudes/}{web})

\end{itemize}
Annual conference series:

\begin{itemize}%
\item \emph{\href{https://indico.cern.ch/event/750565/timetable/#20190701.detailed}{Amplitudes 2019}}

\end{itemize}
\hypertarget{analytic_methods}{}\subsubsection*{{Analytic methods}}\label{analytic_methods}

\begin{itemize}%
\item Ruth Britto, \emph{Loop amplitudes in gauge theories: modern analytic approaches} (\href{http://arxiv.org/abs/1012.4493}{arXiv:1012.4493})


\item [[Zvi Bern]], [[Lance Dixon]], [[David Kosower]], \emph{On-Shell Methods in Perturbative QCD} (\href{http://arxiv.org/abs/0704.2798}{arXiv:0704.2798})


\item [[Joseph Polchinski]], [[Matthew Strassler]], \emph{Hard Scattering and Gauge/String Duality}, Phys.Rev.Lett.88:031601,2002, (\href{http://lanl.arxiv.org/abs/hep-th/0109174}{arXiv:hep-th/0109174})



\end{itemize}
See also at \emph{[[string theory results applied elsewhere]]} and at \emph{[[motivic multiple zeta values]]}.

\hypertarget{in_super_yangmills_theory}{}\subsubsection*{{In super Yang-Mills theory}}\label{in_super_yangmills_theory}

In [[super Yang-Mills theory]] (and there in particular in the [[planar limit]] of [[N=4 D=4 super Yang-Mills theory]]) scattering amplitudes enjoy special symmetry properties, some of which can be used to extract information about scattering amplitudes in non-supersymmetric theories (see also at \emph{[[amplituhedron]]}):

\begin{itemize}%
\item [[Nima Arkani-Hamed]], Jacob L. Bourjaily, Freddy Cachazo, Alexander B. Goncharov, [[Alexander Postnikov]], Jaroslav Trnka, \emph{Scattering Amplitudes and the Positive Grassmannian} (\href{http://arxiv.org/abs/1212.5605}{arXiv:1212.5605})


\item [[Nima Arkani-Hamed]], Jaroslav Trnka, \emph{The Amplituhedron}, \href{http://arxiv.org/abs/1312.2007}{arxiv/1312.2007}



\end{itemize}
\hypertarget{in_string_theory_and_higher_supergravity}{}\subsubsection*{{In string theory and higher supergravity}}\label{in_string_theory_and_higher_supergravity}

\begin{itemize}%
\item Wieland Staessens, Bert Vercnocke, \emph{Lectures on Scattering Amplitudes in String Theory} (\href{http://arxiv.org/abs/1011.0456}{arXiv:1011.0456})


\item [[Michael Green]], \emph{Properties of low energy graviton scattering amplitudes}, June 2010 (\href{http://string.lpthe.jussieu.fr/cargese/2010/talks/green_cargese2010.pdf}{pdf})



\end{itemize}
For more see at \emph{[[string scattering amplitude]]}.

\hypertarget{motivic_structure}{}\subsubsection*{{Motivic structure}}\label{motivic_structure}

Motivic structures in scattering amplitudes (see at \emph{[[motives in physics]]}) are discussed for instance in

\begin{itemize}%
\item John Golden, Alexander B. Goncharov, Marcus Spradlin, Cristian Vergu, Anastasia Volovich, \emph{Motivic Amplitudes and Cluster Coordinates} (\href{http://arxiv.org/abs/1305.1617}{arXiv:1305.1617})

\end{itemize}
See also the references at \emph{[[period]]}.

[[!redirects scattering amplitudes]]

[[!redirects Feynman amplitude]] [[!redirects Feynman amplitudes]]



\end{document}