[FOM] Question about theoretical physics

Colin McLarty colin.mclarty at case.edu
Tue Feb 26 12:31:47 EST 2013

In fact the Clay Institute puts it more sharply that Neumaier does.
They say quantum Yang Mills theory actually does not yet exist as a
precise mathematical theory:

> Quantum Yang-Mills theory is now the foundation of most of elementary particle
> theory, and its predictions have been tested at many experimental laboratories,
> but its mathematical foundation is still unclear. ... it still has not been understood
> from a theoretical point of view. Progress in establishing the existence of the
> Yang-Mills theory and a mass gap and will require the introduction of fundamental
> new ideas both in physics and in mathematics.

Likely enough this was written by Jaffe, or by editors working from
his text.  But I do not believe the point would surprise anyone in


On Tue, Feb 26, 2013 at 11:25 AM, Arnold Neumaier
<Arnold.Neumaier at univie.ac.at> wrote:
> On 02/25/2013 09:24 PM, Jay Sulzberger wrote:
>>    Is there a consistent theory of QED, consistent to the usual
>>    standard of professors of mathematics?
>> To repeat: Experts disagree as to whether there has been
>> published a consistent theory of QED.  There is further
>> disgareement as to whether such a theory is possible without some
>> stuff most would consider not part of QED.
> Experts agree that there exists a consistent theory of QED that predicts an
> asymptotic power series in the fine structure constant alpha
> for the anomalous magentic moment of the electron (and for other physical
> quantities such as the Lamb shift, the positronium lifetime, etc.). It is
> based on renormalization and can be nicely described mathematically in terms
> of the work by Kreiner mentioned in the discussion.
> Experts also agree that there is currently no consistent theory of QED
> that predicts actual values for the anomalous magentic moment of the
> electron (etc.). This would require a nonpertative definition of QED in
> logically impeccable terms, which is one of the big unsolved problems in
> theoretical physics. (A Clay millenium prize is offered for the
> solution of another quantum field theory, which experts think is easier to
> construct than QED.)
> Arnold Neumaier
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