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S9f. Are protons described by QED?
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The traditional field equations of quantum electrodynamics (QED),
which can be found in any textbook on quantum field theory, describe
only electrons, positrons, and photons, but not protons, although
the latter have electromagnetic interactions.
The reason is that, unlike free electrons and positrons, free protons
do not obey the Dirac equation since they have form factors which are
(unlike for electrons and positrons) determined not only by interactions
with photons, but primarily by the inner structure of the proton.
Thus even bare protons cannot be understood as point particles, which
makes standard QED equations inapplicable.
To understand the proton's frm factors from first principles needs
quantum chromodynamics (QCD) - and even then they are imperfectly
understood.
In the traditional QED treatment of molecules and their interaction
with light, protons and other nuclei are typically treated as classical
sources of electromagnetic fields when determining the structure of
the electron. (The resulting effective potential between the
nuclear positions is quantized afterwards if a full classical treatment
is not adequate). This gives excellent agreement with experiment,
in particular for the hydrogen atom.
Of course, one can tread QED together with a proton field as an
effective (and nonrenormalizable) theory, in which in addition to the
Dirac equation for the bare electrons there is a Dirac-like equation,
modified by the form factors, for the bare protons. To describe atoms
correctly, one needs also fields for neutrons and mesons, and
appropriate interaction terms between them, leading to quantum
hadrodynamics (plus QED). This accounts for all practically
relevant properties of atoms (including nuclear fission and fusion).