nLab
holonomic quantum field

Contents

What is this about

There is no single mathematical idea expressed here yet!

The Kyōto school of mathematical physics (Jimbo, Miwa, Sato etc.) in mid 1970-s discovered a nontrivial connection between the theory of isomonodromic deformations of differential equations (and closely related integrable systems!) and the theory of a special class of quantum field theories (whose construction heavily relies upon Clifford algebras and Clifford groups). This subject lives under the title holonomic quantum fields. The work is also relevant to the study of Painlevé transcendents.

Idea: Somebody should figure it out

References

There is a series of longer articles called Holonomic quantum fields I-V (mainly Publ. RIMS) and longer series of shorter articles called Studies in holonomic quantum fields I-XVI (the latter can be found at project euclid, see link).

One of the primary ideas stems from an observation of