Re: Normal ordering and VEV subtraction



> I would not have expected the level of rigor to be higher than at the
> level of perturbation theory.

At the level of pertrubation theory OPE for given operator productcan be derived
by direct computation of Feynman diagrams.

> I'd be happy for a reference where such a
> derivation is given.

Classical most cited references are:

1) Nonlagrangian Models Of Current Algebra. K.G. Wilson, Phys.Rev. 179 (1969) 1499
2) K.G. Wilson and W. Zimmermann, Commun.Math.Phys. 24 (1972) 87

But they are so old. I don know more fresh papers.

> > Yes, path integral picture is not rigorous proof. But it give nice
> > intuitive motivation for OPE in the standart QFT.
>
> While being non-rigorous, since there is a non-rigorous equivalence
> between the path integral and the operator pictures.

Troubles only in cases with non trivial vacuum. But, for example,in QCD widely used hypothesis of
quark-hardron duality. This can
viewed as manifestation of equivalence of path integral and Fock space
pictures. Of course this only applicable in phenomenological level.

> What's not clear to
> me is how to translate the non-rigorous motivation of the OPE in a path
> integral formalism to a non-rigorous motivation of the OPE in the Fock
> space picture.

In my opinion, Fock space OPE arise simple by proposition that any
dynamic can not make singularity in operator product as in non interacting
case. In non singular case we can simple use Taylor expantion ;-)
Most interesting topic is possible anomalies in operator product. For
example, well known Casimir force is anomaly in normal ordering
procedure.


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