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\section*{quantum electrodynamics}

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

\hypertarget{algebraic_qunantum_field_theory}{}\paragraph*{{Algebraic Qunantum Field Theory}}\label{algebraic_qunantum_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{definition}{Definition}\dotfill \pageref*{definition} \linebreak
\noindent\hyperlink{properties}{Properties}\dotfill \pageref*{properties} \linebreak
\noindent\hyperlink{related_concepts}{Related concepts}\dotfill \pageref*{related_concepts} \linebreak
\noindent\hyperlink{references}{References}\dotfill \pageref*{references} \linebreak
\noindent\hyperlink{original_articles}{Original articles}\dotfill \pageref*{original_articles} \linebreak
\noindent\hyperlink{review}{Review}\dotfill \pageref*{review} \linebreak
\noindent\hyperlink{phenomenology}{Phenomenology}\dotfill \pageref*{phenomenology} \linebreak


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

\emph{Quantum electrodynamics} (``QED'') is the [[perturbative quantum field theory]] of the [[electromagnetic field]] coupled to a [[Dirac field]] via the [[electron-photon interaction]]: it describes the [[quantum theory]] of [[photons]] and [[electrons]].

\hypertarget{definition}{}\subsection*{{Definition}}\label{definition}

The [[Lagrangian density]] defining QED is the [[sum]] of

\begin{enumerate}%
\item the [[free field]] contribution of the [[electromagnetic field]];


\item the [[free field]] contribution of a [[Dirac field]];


\item the [[electron-photon interaction]] term with [[coupling constant]] given by the [[fine structure constant]].



\end{enumerate}
See at \emph{[[A first idea of quantum field theory]]} \href{A+first+idea+of+quantum+field+theory#LagrangianQED}{this example}.

The underlying [[free field theory]] admits a [[quantization]] via the corresponding [[Wick algebra]]. QED is, by definition, the [[perturbative quantum field theory]] obtained from this by finding a perturbative [[S-matrix]] for the [[electron-photon interaction]].

As a result, [[scattering amplitudes]] for [[electron-photon interactions]] in QED are then expressed in terms of [[Feynman amplitudes]]:

[[!include Feynman diagrams in causal perturbation theory -- summary]]

\hypertarget{properties}{}\subsection*{{Properties}}\label{properties}

\begin{itemize}%
\item [[anomalous magnetic moment of the electron]]


\item [[Lamb shift]]


\item [[Casimir effect]]


\item [[axial anomaly]]



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

\begin{itemize}%
\item [[fine structure constant]]


\item [[photon propagator]]


\item [[quantum field theory]]

\begin{itemize}%
\item [[scalar field]]


\item [[gauge theory]]

\begin{itemize}%
\item \textbf{QED}


\item [[QCD]], [[quantization of Yang-Mills theory]]



\end{itemize}


\end{itemize}


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

\hypertarget{original_articles}{}\subsubsection*{{Original articles}}\label{original_articles}

The term ``quantum electrodynamics'' is due to

\begin{itemize}%
\item [[Paul Dirac]], \emph{The quantum theory of emission and absorption of radiation}, Proc. Roy. Soc. London A 114, 243, 1927 (\href{http://inspirehep.net/record/42586?ln=en}{spire}, \href{http://wwwhome.lorentz.leidenuniv.nl/~boyarsky/media/Proc.R.Soc.Lond.-1927-Dirac-243-65.pdf}{pdf})

\end{itemize}
This left some issues with the quantization of the radiation field. These were addressed, and the [[causal propagator]] for the [[electromagnetic field]] was first found in

\begin{itemize}%
\item [[Pascual Jordan]], [[Wolfgang Pauli]], \emph{Zur Quantenelektrodynamik ladungsfreier Felder}, Zeitschrift f\"u{}r Physik 47, 151 (1928)

\end{itemize}
A comprehensive, albeit informal, theory of QED and of [[perturbative quantum field theory]] in general was eventually developed by

\begin{itemize}%
\item [[Schwinger-Tomonaga-Feynman-Dyson]], 1940s

\end{itemize}
For more on the history see

\begin{itemize}%
\item [[Rudolf Haag]], \emph{Early papers on quantum field theory (1992-1930)} (\href{https://link.springer.com/content/pdf/bfm%3A978-3-642-70078-1%2F1%2F1.pdf}{pdf})

\end{itemize}
and (\hyperlink{Scharf95}{Scharf 95, section 0.0}).

Discussion of [[vacuum stability]] in [[QED]] includes

\begin{itemize}%
\item [[Günter Scharf]], \emph{Vacuum stability in quantum field theory}, Nuovo Cim. A109 (1996) 1605-1607 (\href{http://inspirehep.net/record/432208/}{spire:432208})


\item [[Hrvoje Nikolić]], \emph{Physical stability of the QED vacuum}, 2001 (\href{https://arxiv.org/abs/hep-ph/0105176}{arXiv:hep-ph/0105176})



\end{itemize}
The rigorous construction of [[perturbative QFT|perturbative]] QED in [[causal perturbation theory]] is worked out in

\begin{itemize}%
\item \hyperlink{Scharf95}{Scharf 95}

\end{itemize}
and refined to [[perturbative AQFT]] in

\begin{itemize}%
\item [[Michael Dütsch]], [[Klaus Fredenhagen]], \emph{A local (perturbative) construction of observables in gauge theores: the example of QED} , Commun. Math. Phys. 203 (1999), no.1, 71-105, (\href{http://xxx.uni-augsburg.de/abs/hep-th/9807078}{arXiv:hep-th/9807078}).

\end{itemize}
and generalized to possibly non-abelian [[Yang-Mills theory]] in

\begin{itemize}%
\item [[Stefan Hollands]], \emph{Renormalized Quantum Yang-Mills Fields in Curved Spacetime}, Rev. Math. Phys. 20:1033-1172, 2008 (\href{https://arxiv.org/abs/0705.3340}{arXiv:0705.3340})

\end{itemize}
The [[weak adiabatic limit]] of QED was established in

\begin{itemize}%
\item P. Blanchard and R. Seneor, \emph{Green’s functions for theories with massless particles (in perturbation theory)}, Ann. Inst. H. Poincaré Sec. A 23 (2), 147–209 (1975) (\href{http://www.numdam.org/item?id=AIHPA_1975__23_2_147_0}{Numdam})


\item [[Paweł Duch]], \emph{Massless fields and adiabatic limit in quantum field theory} (\href{https://arxiv.org/abs/1709.09907}{arXiv:1709.09907})



\end{itemize}
The [[local net of algebras of observables]] and hence the [[algebraic adiabatic limit]] was worked out in

\begin{itemize}%
\item \hyperlink{DuetschFredenhagen98}{Dütsch-Fredenhagen 98}

\end{itemize}
Further discussion of the [[adiabatic limit]] and [[infrared divergences]] includes

\begin{itemize}%
\item Daniel Kapec, Malcolm Perry, Ana-Maria Raclariu, [[Andrew Strominger]], \emph{Infrared Divergences in QED, Revisited}, Phys. Rev. D 96, 085002 (2017) (\href{https://arxiv.org/abs/1705.04311}{arXiv:1705.04311})

\end{itemize}
\hypertarget{review}{}\subsubsection*{{Review}}\label{review}

Traditional discussion includes

\begin{itemize}%
\item [[Radovan Dermisek]], \emph{Quantum Electrodynamics (QED)} (\href{http://www.physics.indiana.edu/~dermisek/QFT_09/qft-II-5-4p.pdf}{pdf}, [[DermisekQED.pdf:file]])


\item [[Hitoshi Murayama]], \emph{Quantum Electrodynamics} (\href{http://hitoshi.berkeley.edu/221B-S02/QED.pdf}{pdf})


\item [[Eberhard Zeidler]], \emph{Quantum field theory II: Quantum electrodynamics -- A bridge between mathematicians and physicists}, Springer (2009)


\item Einan Gardi, lectures 19, 20 of \emph{\href{https://www2.ph.ed.ac.uk/~egardi/MQFT/}{Modern Quantum Field Theory}}, 2015 (\href{https://www2.ph.ed.ac.uk/~egardi/MQFT/MQFT_2015_lecture_19_20.pdf}{pdf})



\end{itemize}
Mathematically rigorous discussion in [[causal perturbation theory]]/[[perturbative AQFT]] is in

\begin{itemize}%
\item [[Günter Scharf]], \emph{[[Finite Quantum Electrodynamics -- The Causal Approach]]}, Berlin: Springer-Verlag, 1995, 2nd edition


\item [[Michael Dütsch]], chapter 5 of \emph{[[From classical field theory to perturbative quantum field theory]]}, 2018

following (\hyperlink{DuetschFredenhagen98}{Dütsch-Fredenhagen 98})



\end{itemize}
\hypertarget{phenomenology}{}\subsubsection*{{Phenomenology}}\label{phenomenology}

Comparison to [[experiment]] is reviewed in

\begin{itemize}%
\item \emph{Tests of QED} (\href{http://edu.itp.phys.ethz.ch/hs10/ppp1/PPP1_6.pdf}{pdf})

\end{itemize}
Specifically via the [[Lamb shift]]:

\begin{itemize}%
\item Savely G. Karshenboim, D. I. Mendeleev, \emph{The Lamb Shift of Hydrogen and Low-Energy Tests of QED} (\href{https://arxiv.org/abs/hep-ph/9411356}{arXiv:hep-ph/9411356})

\end{itemize}
[[!redirects quantum electrodynamics]] [[!redirects quantum electro dynamics]] [[!redirects QED]]



\end{document}