Jürg Fröhlich

Selected writings

On the Jones polynomial via Chern-Simons theory:

On non-perturbative quantum field theory:

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

On supersymmetric quantum mechanics from the point of view of spectral geometry (“noncommutative geometry”):

and with an eye towards the superstring via 2-spectral triples:

Another survey is

On quantum probability theory and the operator algebra-foundations for quantum physics:


From Fröhlich 92, p. 11, on laying foundations for perturbative string theory via rigorous formulation of 2d SCFT in terms of conformal nets/2-spectral triples 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 III_1 von Neumann algebras – to be a little technical – indexed by intervals of the circle with non-empty 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.

category: people

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