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Chapter 7
Quantum Electrodynamics
7.1 Introduction
In this chapter we shall start to work our way to realistic theories about the
actual elementary particles encountered in nature 1 . All elementary particles
seen so far have nonzero spin, apart from the newly-discovered Higgs boson.
We shall defer the discussion of charged spin-1 particles to a later chapter ; at
this point we shall only discuss how to set up a consistent theory of spin-1/2
particles (charged leptons and/or quarks) and photons. This is the theory of
quantum electro-dynamics, or QED.
7.2 Setting up QED
7.2.1 The QED vertex
Since the propagators of spin-1/2 particles and of the massless spin-1 photon
have already been fixed, the only ingredient which we still have to determine is
the coupling between them ; and on this coupling rests the burden of ensuring
the current-conservation requirement as embodied in Eq.(6.58). The vertex
coupling Dirac particles must have one upper, and one lower Dirac index : and
since the photon is involved, it must also carry a Lorentz index. The simplest,
and – as we shall see – indeed the correct form of the vertex is that of a Dirac
matrix. We therefore propose the following Feynman rule :
1 It may of course be possible that the elementary particles discussed in this text are not
truly elementary and that a yet deeper level of substructure will be discovered. In that case,
please insert in whatever follows the addendum (A.D. 2012).
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