[FOM] Question about theoretical physics

Arnold Neumaier Arnold.Neumaier at univie.ac.at
Tue Feb 26 03:18:03 EST 2013

On 02/25/2013 02:04 AM, Jay Sulzberger wrote:
> [The sum of a power series with convergence radius zero is logically]
> Not necessarily meaningless.  One can define other "summation
> methods".  Work of the past about fifteen years connects certain
> classical summation methods with old puzzlements about what
> "renormalization by iterated subtractive over and under
> corrections" using Feynman diagrams is:

The problem is that any fixed summation methods give the same results
for the asymptotic expansion of g(alpha)+c*e^{-1/alpha^2} for any c (as 
these have the same asymptotic expansion). Hence there is no guarantee 
at all that the result of the summation method corresponds to the
''true'' value predicted by a future nonperturbative formulation of QED.

For example, to use Borel summation one needs to know (or pretend to 
know) analytic properties in a cone with vertex 0, properties that are 
most likely invalid for QED.

This is completely independent of the various renormalization tools.

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