Re: The Solution To The Ultraviolet Divergence Problem

"Rock Brentwood" <markwh04@xxxxxxxxx> wrote in message news:1177628435.027156.114390@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

[...]
The result -- in the Minkowski space limit near a point-like source --
will be a differential equation of the form
epsilon r^3 (r log epsilon)'' = -2 A^2
for some constant A.

This can exhibit screening or anti-screening behavior, with an
asymptotic expansion
epsilon = epsilon_0 + B/r,
where B can be freely set. In the limit as r -> 0, it exhibits the
asymptotic behavior
epsilon = A/r^2.

For a point-like solution D = e/(4 pi r^2), E = e/(4 pi epsilon r^2),
this yields a finite energy density near the origin.

The size of the cutoff introduced by this extra "vacuum polarization"
field turns out to be on the order of the Planck length.

I think you were doing pretty good up 'til the end here. How do you possibly calculate the cutoff is on the order of the Planck length? If g_55 is variable, why can't the cutoff be variable and actually much bigger than Planck length. Like say, closer to the electroweak scale?

Best,

Fred Diether

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