## A shocking step

Lorenz von Smekal has been one of the proponents of the functional approach to the understanding of infrared Yang-Mills theory. He is currently working at University of Adelaide where a lot of important work on lattice computations is performed. Today on arxiv appeared a paper by him (see here). I would like to report here his words in the introduction

“Without infrared enhancement of the ghosts in Landau gauge, the global gauge charges of covariant gauge theory are spontaneously broken. Within the language of local quantum field theory the decoupling solution can thus only be realised if and only if it comes along with a Higgs mechanism and massive physical gauge bosons. The Schwinger mechanism can in fact be described in this way, and it can furthermore be shown that a non-vanishing gauge boson mass, by whatever mechanism it is generated, necessarily implies the spontaneous breakdown of global symmetries.”

The “decoupling solution” cited here is the one currently seen on lattice computations having a finite gluon propagator at zero momenta and a ghost propagator behaving like a free particle without any fixed point in the running coupling. The point here is that, in this paragraph, the truth about the real situation of Yang-Mills theory in the infrared is simply exposed. Classical solutions exist that display such dynamical generation of mass for the massless scalar field theory and Yang-Mills theory (see here) and a quantum field theory can be built with them making the above argument truly consistent.

But the point to be emphasized here is the proposal of von Smekal arriving to present a modification of lattice computations. His proposal relies on a recent work done with Andre Sternbeck (see here) where they study the limit $\beta\rightarrow\infty$ of the Yang-Mills theory. Indeed, in this limit they recover the results obtained by functional methods that disagree with lattice computations. Again, they simply freeze the dynamics and get meaningless results as also happens when one compares D=1+1 Yang-Mills theory with no dynamics and the D=4 case. Besides, recent QCD computations on the lattice, relying on known formulations of the Yang-Mills side, give too striking results to go to look for reformulations (see my post).

My view is that functional methods are generally useless. Also when the right solution is hit, of course numerically, one is not able to do any kind of real calculation in QCD. In physics this means that no true understanding is reached. One of the points that should have warned people working with functional methods is that no mass gap is ever obtained and there is no way to recover the low-energy phenomenology of QCD. But having a mass gap produces immediately a Nambu-Jona-Lasinio model from QCD from the ratio $g^2$ to the square of the mass gap itself and this is a real understanding as Nambu-Jona-Lasinio model gives a lot of comprehension of low energy phenomenology.

I think this paper is worth an in depth reading as it contains several pieces of true awareness. My criticisms should not be of any concern for such a good work.

This site uses Akismet to reduce spam. Learn how your comment data is processed.