Some months ago a paper of mine was rejected by an editor of JHEP in a few minutes as this person pretended that my choice of the initial solution of Yang-Mills theory to build a strong coupled QFT was “ad hoc”. The point is that I assumed that the work of George Savvidy and Sergei Matinyan was universally known. These authors proved without any doubt that Yang-Mills mechanics is generally chaotic and so, if I would like to use a gradient expansion to build a QFT I am in a serious difficulty as a QFT built on chaotic solutions cannot exist.
Matinyan summed up most of these results here and was kind enough to cite a paper of mine. So, we all known that for small perturbations one can use free particle solutions but what one can do for the strong coupling case, what are the solutions to start from?
In this post I showed that a non chaotic classical solution exists that has the property to manifest a massive dispersion relation. This classical solution is obtained when one takes all the components of the Yang-Mills to be equal (see here). This is a kind of “replica trick”, that is, we replicate a massless scalar field a number of times enough to solve exactly Yang-Mills equations of motion. So, if we want the quantum theory to produce a mass gap, this is the only choice we have. A QFT can be straightforwardly built and we can manage strong interactions in the strong coupling limit.
So, aside from rejection records, there are serious reasons for satisfaction as a meaningful theory exists that is general enough to treat a quantum field in the strong coupling limit due also to the relevant contribution of Matinyan and Savvidy. The starting point is anyhow a gradient expansion. We will have more to say about in future posts.