Simple (but wrong) argument for the generality of positive beta-functions In the introduction (page 5) of Supersymmetry and String Theory: Beyond the Standard Model by Michael Dine (Amazon, Google), he says

(Traditionally it was known that) the interactions of particles typically became stronger as the energies and momentum transfers grew. This is the case, for example, in quantum electrodynamics, and a simple quantum mechanical argument, based on unitarity and relativity, would seem to suggest it is general.

Of course, he then goes on to talk about Yang-Mills theory and the discovery of negative beta-functions and asymptotic freedom. But it is the mention of the simple but wrong argument that caught my attention.
So, does anyone know what this simple argument is?
And how is it wrong?
 A: Michael Dine's response, quoted with permission: 

I now have to think back, but the argument in QED is based on the spectral representation ("Kallen-Lehman representation").  The argument purports to show that the wave function renormalization for the photon is less than one (this you can find, for example, in the old textbook of Bjorken and Drell, second volume; it also can be inferred from the discussion of the spectral function in Peskin and Schroder).  This is enough, in gauge theories, to show that the coupling gets stronger at short distances.  The problem is that the spectral function argument assumes unitarity, which is not manifest in a covariant treatment of the gauge theory (and not meaningful for off-shell quantities).  In non-covariant gauges, unitarity is manifest, but not Lorentz invariance, so the photon (gluon) renormalization is more complicated.  In particular, the Coulomb part of the gluon ($A^0$) is not a normal propagating field.  

A: This is a temporary answer in order to store the generous bounty that Ron offered. When a proper answer to this question is given, I will transfer the 500 rep points (assign an equal bounty) to that answer.
Going by the totalitarian principle of quantum mechanics / quantum field theory, since this move is not explicitly forbidden, it must be compulsory.
A: I may be wrong, but the following remark in this PDF (PHYSICS REPORTS 167, No. 5 (1988) 241—320) may be relevant:

Then [2.1] it follows that if $[x, y] = \Delta_+(y-x)$ possesses properties implied by the Garding—Wightman axioms, then a set of $W_n$ defined by $$W_n\left(x, \dots , x_n\right) = \left[x_1, \dots , x_n \right]  \tag{2.6}$$obeys these axioms and the associated field theory is a generalized free field, i.e., it is a trivial theory.

Reference [2.1] there is B. Simon, The $P(\varphi)^2$
Euclidean (Quantum) Field Theory (Princeton, 1974).
By the way, you can just ask the author, M. Dine. Sometimes asking the author is the only way to sort out what (s)he wrote:-). I remember I found a book containing a result I had recently obtained myself, but without any proof. I e-mailed one of the two authors of the book and asked for the relevant reference. It took me a couple of months, but eventually he advised me that they meant something different from the result that I obtained, so my result was new:-)
