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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeDec 19th 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexUnder "Selected writings" I have added pointer to * [[Jürg Fröhlich]], _Non-perturbative quantum field theory -- Mathematical Aspects and Applications_, Advanced Series in Mathematical Physics, World Scientific 1992 ([doi:10.1142/1245](https://doi.org/10.1142/1245)) and then I added quote of the following passage, from p. 11, on laying foundations for [[perturbative string theory]] via rigorous formulation of [[2d SCFT]] in terms of [[conformal nets]] or similar: > I still have hopes, perhaps romantic ones, that [[string theory]], or something inspired by it, will come back to life again. I believe it is interesting to attempt to formulate string theory in an "invariant" way, quite like it is useful to formulate geometry in a coordinate-independent way. One might, for example, start with a family $\mathcal{F}$, of [[von Neumann algebra factor|hyperfinite type $III_1$ von Neumann algebras]] -- to be a little technical -- [[conformal net|indexed by]] intervals of the circle with non-emptry complement (or of the super-circle). It may pay to formulate the starting point using the language of [[sheaves]]. $[...]$ This structure determines a [[braided monoidal category|braided monoidal]] [[C*-category]] with unit, ...; briefly, a quantum theory. From a combination of such [[tensor categories]] (left and right movers) one would attempt to reconstruct (symmetries of) _physical space-time_. String amplitudes would correspond to [[morphisms|arrows]] ([[intertwiners]]) of the [[tensor category]]. $[...]$ it would provide a general way of thinking about string theory that does not presuppose knowing the target space-time of the theory. <a href="https://ncatlab.org/nlab/revision/diff/J%C3%BCrg+Fr%C3%B6hlich/5">diff</a>, <a href="https://ncatlab.org/nlab/revision/J%C3%BCrg+Fr%C3%B6hlich/5">v5</a>, <a href="https://ncatlab.org/nlab/show/J%C3%BCrg+Fr%C3%B6hlich">current</a>

   Under “Selected writings” I have added pointer to

   • Jürg Fröhlich, Non-perturbative quantum field theory – Mathematical Aspects and Applications, Advanced Series in Mathematical Physics, World Scientific 1992 (doi:10.1142/1245)

   and then I added quote of the following passage, from p. 11, on laying foundations for perturbative string theory via rigorous formulation of 2d SCFT in terms of conformal nets or similar:

   I still have hopes, perhaps romantic ones, that string theory, or something inspired by it, will come back to life again. I believe it is interesting to attempt to formulate string theory in an “invariant” way, quite like it is useful to formulate geometry in a coordinate-independent way. One might, for example, start with a family $\mathcal{F}$, of hyperfinite type $III_1$ von Neumann algebras – to be a little technical – indexed by intervals of the circle with non-emptry complement (or of the super-circle). It may pay to formulate the starting point using the language of sheaves. $[...]$ This structure determines a braided monoidal C*-category with unit, …; briefly, a quantum theory. From a combination of such tensor categories (left and right movers) one would attempt to reconstruct (symmetries of) physical space-time. String amplitudes would correspond to arrows (intertwiners) of the tensor category. $[...]$ it would provide a general way of thinking about string theory that does not presuppose knowing the target space-time of the theory.

   diff, v5, current