[FOM] Question about theoretical physics

[Colin McLarty]

A lot of people have written very good more detailed comments on this.
 I just want to add Arthur Jaffe's summary.  This has been the
consensus among nearly everyone involved, for decades even as there
has been huge technical progress:

"the success of relativistic field theory calculations and of
perturbative renormalization also led to a logical puzzle: is there
any physically-relevant, relativistic quantum field theory that is
also mathematically consistent? ....  For the time being, all these
methods remain beyond the realm of full understanding."  (CONSTRUCTIVE
QUANTUM FIELD THEORY, on line at
http://www.arthurjaffe.com/Assets/pdf/CQFT.pdf).

Here "constructive" means "construable" as in "construable in
physically-relevant terms."

colin





On Fri, Feb 22, 2013 at 12:39 PM, Nik Weaver <nweaver at math.wustl.edu> wrote:
>
> Joe Shipman wrote:
>
>> If my account is correct, then even the supposedly well-established theory
>> of Quantum Electrodynamics does not have a valid mathematical foundation,
>> because it unjustifiably assumes convergence of the relevant series.
>
>
> Yes, at least for now QED in 4 spacetime dimensions does not have a
> valid mathematical foundation.  This is considered one of the major
> open problems in mathematical physics.  The Wikipedia article on
> "Constructive quantum field theory" is a good place to start (here
> "constructive" is used in a rather odd way, to mean "coming up with
> a mathematical model which can justify the physical recipes").
>
> Nik
>
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