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From: brooks@lll-crg.ARPA (Eugene D. Brooks III)
Newsgroups: net.sf-lovers,net.physics
Subject: Re: Re: Renormalization (relativity, etc.)
Message-ID: <605@lll-crg.ARPA>
Date: Fri, 24-May-85 00:59:34 EDT
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Posted: Fri May 24 00:59:34 1985
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> the two infinities cancel, and the measured mass of the electron
> is perfectly finite.  Most physicists believe that this effect
> is an artifact of the way the calculation is done (as above);
> if we knew the "correct" way [the equivalent of Gauss' law, above]
> (not perturbation theory--an approximation), we could do the whole
> calculation without infinities.

There are several examples of this in solvable quantum field models.
One of them is the case of a very massive Fermion coupled to a Bose field
via a Yukawa coupling.  The "Bare" interacting particles have infinities
when pertubation theory is used.  The model can be analytically solved to
obtain the "Dressed" physical particles and a finite theory.  The result is
a free Bose field and Fermions that interact through a static potential.
This model is a very good example of renormalization via a solvable theory.

A complete chapter on the model can be found in
S. Schweber, "Relativistic Quantum Field Theory," around p. 339-351