[FOM] Question about theoretical physics

Arnold Neumaier Arnold.Neumaier at univie.ac.at
Wed Mar 6 03:00:11 EST 2013

On 03/02/2013 07:57 PM, Joe Shipman wrote:

> Can Professor Neumaier, or any other theoretical physicist, provide a link the following much simpler pieces of documentation?
> 1) a method for enumerating Feynman diagrams relevant to the calculation of the magnetic moment of the electron

This is not how it is done. The actual high order computations involve 
an expansion in powers of both alpha and 1/c^2, and the choice of the 
temrs evaluated is based on heuristics which ones are likely to 
influence the result. The actual method used is NRQED, not the standard 
Feynman series expansion. Figuring out what precicesly has been done or 
needs to be done to replicate the results is itself a research project 
that only those are interested to do who actually want to do the 
checking (usually because they have an alternative in mind that might 
work better).

> 2) a high-level description of the process by which the value of a Feynman integral for *one specific nontrivial Feynman diagram* is numerically approximated

The contribution of a single Feynman integral is infinite, except for 
the lowest order (zero loop) tree level disarams. Finite values arise 
form linear combinations of such contributions that have a definite 
finite value in the renormalization limit.

The closest approximation to what you want is in the work by Kreiner, 
but this is itself quite abstract (involving Hopf algebras) and 
acccessible only to a small part of theretical physicists.

Arnold Neumaier

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