Bootstrapping quantum Yang-Mills with concrete axioms

[BohmianRealist]

TL;DR

Are there any simple examples for constructing quantum fields using the Euclidean axiom approach?

From: https://en.wikipedia.org/wiki/Axiomatic_quantum_field_theory

The first set of axioms for quantum field theories, known as the Wightman axioms, were proposed by Arthur Wightman in the early 1950s. These axioms attempt to describe QFTs on flat Minkowski spacetime by regarding quantum fields as operator-valued distributions acting on a Hilbert space.

But, that seems like a fairly abstract place to begin the kind of QFT construction that was asked of us by Witten in 2012:

The title should possibly refer to "what we can and cannot hope to prove". The reason for giving this talk is that having a clear picture of what one can and cannot hope to prove may help with strategies for proving what one can prove. Of course, implicit is a belief that the study of quantum Yang-Mills should be reinvigorated. Personally I think the relation between mathematics and physics will remain unsatisfactory unless the program of constructive field theory is reinvigorated in some form.

At the bottom of that page on axiomatic QFT are the "Euclidean CFT axioms":

These axioms (see e.g. [1]) are used in the conformal bootstrap approach to conformal field theory in

. They are also referred to as Euclidean bootstrap axioms.

Are there any examples of concrete bootstrapping of QFT, so that anyone can follow along, ala Euclid's Elements?

 

[A. Neumaier]

At the bottom of that page on axiomatic QFT are the "Euclidean CFT axioms":

Are there any examples of concrete bootstrapping of QFT, so that anyone can follow along, ala Euclid's Elements?

The book by Glimm and Jaffe gives full details for constructing 2-dimensional interacting quantum fields that way. (But this is still very far away from 4D quantum Yang-Mills.)

 

[BohmianRealist]

A., thanks... Just bought the e-book and now reading!