Re: "4/3 Problem" Resolution (fwd), comment on

[Jack Uretsky <jlu@HEP.ANL.GOV>]

On Wed, 16 May 2001, David Rutherford wrote (in relevant part):
        [Uretsky had written]
> >        Specifying curl(A) is not the same as specifying A.  Since the
> > curl of a gradient is zero, I can add any gradient to A without changing
> > the value of the curl.  But there is an infinity of gradients that will
> > change the value of div(A).  That's part of the principal of gauge
> > invariance.
>
> Then it's incumbant on you to find a condition under which the value of
> div(A) is not changed or you must dump the concept of gauge invariance,
> because div(A) is definitely specified. In this three-dimensional, time
> invariant case, gauge invariance is only possible if the condition
>
> d^2(/\)/dx^2 +  d^2(/\)/dy^2 +  d^2(/\)/dz^2 = 0
>
> is satisfied. If you don't choose to accept that condition, then you have to
> abandon the validity of gauge invariance for this case. Periodisimo.

        Ahh, there we have it.  David's quarrel is with gauge invariance.
        But the principle of gauge invariance derives from the statement
that only the fields are physical.  The potentials (A and phi) are not.
        Stated otherwise, it is the Maxwell equations, expressed in terms
of the E and B fields that completely describe classical electrodynamics.
David evidently wants to make some condition on div(A) an addition to
the Maxwell Equations (that is, a gauge-fixing condition).  Such a
condition would have far-reaching consequences, because all accepted
calculations to date insist on gauge invariance.  A recent relevant
example is the eight order (in charge) calculation of the muon
g-2 done over the years by Kinoshita and others.

                                                Regards,
                                                        Jack

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