Abstract
As the name indicates, quantum electrodynamics (QED) is the quantised counterpart of classical electrodynamics and it describes the interaction of the electromagnetic field with charged matter particles. In the Standard Model (Chap. 9) the matter particles are leptons and quarks. Here we restrict ourselves to the simplest and historically most relevant case of the matter particles and only deal with electrons and, as always in quantum field theory, their antiparticles, the positrons.
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- 1.
One reason for this “simplicity” is that we use here, other than elsewhere in the book, the usual convention of particle physicists expressing actions in units of \(\hbar \) and velocities in units of c. In a notation that has the tendency to confuse the layman: \(\hbar = c = 1\). \(\partial _\mu \) stands for the partial derivative \(\partial /\partial x^\mu \).
- 2.
For a particle with charge q, e.g., for a quark with charge \(q=2\,e/3\), the electron charge \(- e\) must be replaced by q.
- 3.
\(\gamma ^\mu \,(\mu =0,1,2,3)\) are the four-dimensional Dirac matrices, corresponding to the four components of the field \(\psi (x)\). In (5.1) and (5.2) we use the summation (or Einstein) convention where a sum over twice occurring indices is understood: e.g., \(\gamma ^\mu \partial _\mu \) stands for \(\displaystyle \sum _{\mu =0}^3 \gamma ^\mu \displaystyle \frac{\partial }{\partial x^\mu }\).
- 4.
Under an internal symmetry transformation only the fields but not the space-time coordinates are transformed.
- 5.
We consider unpolarised photons and electrons.
- 6.
The Compton cross section in lowest-order perturbation theory was first calculated by Oskar Klein and Yoshio Nishina (Klein and Nishina 1929).
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Ecker, G. (2019). Quantum Electrodynamics: Prototype of a Quantum Field Theory. In: Particles, Fields, Quanta. Undergraduate Lecture Notes in Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-14479-1_5
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DOI: https://doi.org/10.1007/978-3-030-14479-1_5
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