The authors give a detailed and pedagogically well written proof of
the renormalizability of quantum electrodynamics in four
dimensions. The proof is based on the free expansion of Gallavotti
and Nicolo and is mathematically rigorous as well as impressively
general. It applies to rather general models of quantum field
theory including models with infrared or ultraviolet singularities,
as shown in this monograph for the first time. Also discussed are
the loop regularization for renormalized graphs and the Ward
identities. The authors also establish that in QED in four
dimensions only gauge invariant counterterms are required. This
seems to be the first proof which will be accessible not only to
the expert but also to the student.
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