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added to S-matrix a useful historical comment by Ron Maimon (see there for citation)
Sounds interesting, but what’s the key point? String theory ought to be considered as a S-matrix theory to make best sense of it?
To me a key point is that the ways of the scientific community can be convoluted (reminds me of Nolte’s account of the history of the notion of “phase space”) and that one should trust in genuine understanding and not just the in the current folk lore, as that may be confused in subtle ways over decades. In particular it’s important to know what is actually known, what is just expected.
Yes, perturbative string theory is an S-matrix theory. This is so by definition and by design. The point here is that it is a curious irony of history: first S-matrix theory is overthrown and abandoned in favor of quantum field theory, then later some people start to say that quantum field theory needs to be refined by string theory – which in turn is an S-matrix theory that contradicts the claim that every sensible S-matrix is that of a field theory.
One statement of Maimon that particularly resonated with me is the “…the main S-matrix theory, string theory, is not properly explained and remains completely enigmatic even to most physicists.” This is a feeling that have all the time: so much discussion of string theory in the public domain, and so much confusion about what it really is. It may be all wrong, but not for the alleged reasons most commonly voiced about it.
So I think it’s good to be aware of the history here and beware of common lore without thorough scrutinization.
added a quote from a talk by Weinberg in 2009 to the History-section at S-matrix (search for “Weinberg” to find it)
I have tweaked the Idea-section at S-matrix a little and collected the historical comments in a single History-section and then moved that further towards the end of the entry. Then I copied over the technical discussion of the S-matrix in quantum mechanics and perturbative quantum field theory from the entry interaction picture.
(This means that now these two entries have a considerable overlap. But that seems better than one of the two lacking this basic information. Eventually the entries will grow in different directions.)
If
$\vert \psi(t)\rangle_I \coloneqq \exp\left({\tfrac{- t}{i \hbar} H_{free}}\right) \vert \psi(t)\rangle_S$shouldn’t
$\vert \psi(t) \rangle_S = \exp\left({\tfrac{t}{i \hbar} H}\right) \vert \psi(t) \rangle_I$have $H_{free}$?
Thanks for catching this. Absolutely, as the surrounding text explained, the point is that we have $H_{free}$ here. I have fixed it now.
I have also added another paragraph of text below the definition of the state in the interaction picture, here.
Since that section had been copied (#5) from Dirac interaction picture, those same changes are needed there.
Yes, done now. I have also done a bunch of other edits to this section.
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