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  Glimm and Jaffe's paper on the construction of 2D QFTs

+ 3 like - 0 dislike

I am presently interested in the construction of low-dimensional (2D/3D) QFTs where all the Wightman axioms have been proved and to this end, I started reading the classical paper by Glimm and Jaffe: http://www.jstor.org/stable/1970959?seq=1#page_scan_tab_contents.

The article looks interesting but there are some points that I cannot get. 

For instance, concerning the definition of $y_0$ (the time of the annihilators). In the paragraph below eq. (2.2.6), it is claimed to belong to $\mathbf{Z} + \frac{1}{2}$ (i.e it is a half-integer). But in the second paragraph below (2.2.7), it is said that $y_0 = 0$ for the so-called initial terms. Also, if you look at the details of the contour expansion algorithm in section 2.3 (more precisely, page 610), you'll see $y_0$ is incremented by units, so there seems to be no way to reconcile both statements.

Also, in the proof of lemma 2.4.3 as I understand it, we want to lower bound the separation between $y_0$ and the time of the fields appearing in the Wick monomial $B$. They claim that $\sigma_i \geq 1$ (I inferred that $\sigma_i$ meant this separation by comparing with the proof of the previous lemma, though the notation is never defined AFAIK). But if you merely know $y_0 \in [T - 1, T]$ and $B$ is localized at times greater than $T$, then this separation could be arbitrarily small from my understanding...

Could someone please shed light on these points? Or maybe just give general feedback on the article (as I understood, it is a classic in Axiomatic QFT, the authors are renowned, etc. but it would be great to hear from people who actually read it carefully).

asked May 5, 2018 in Mathematics by IchKenneDeinenNamen (30 points) [ no revision ]

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