====== Yang Mills framework and the 'mass gap' ======

>Almost half a century ago, Yang and Mills introduced a remarkable new framework to describe elementary particles using structures that also occur in geometry. Quantum Yang-Mills theory is now the foundation of most of elementary particle theory, and its predictions have been tested at many experimental laboratories, but its mathematical foundation is still unclear.\\ \\ Source : [[https://www.claymath.org/millennium/yang-mills-the-maths-gap/|Clay Mathematics Institute]]

The 'Standard Model' (SM) of particle physics is completely reliant on Yang-Mills  quantum field theory, which was devised in 1953 as a way of explaining the behaviour of fundamental atomic particles.

It has been spectacularly successful - not only confirmed by computer simulations, but also by countless experiments.

A full mathematical model of the theory, however, has not yet been found.*

In addition, most of the particles have mass, and yet the 'waves' of the 'Yang-Mills field' are assumed to travel at the speed of light. Relativity theory, however, insists that any particle with mass //cannot travel at light speed.//

>The successful use of Yang-Mills theory to describe the strong interactions of elementary particles depends on a subtle quantum mechanical property called the ‘mass gap’: the quantum particles have positive masses, even though the classical waves travel at the speed of light.\\ \\ [ Source as above ]

//Further reading :// A detailed technical description of the [[https://www.damtp.cam.ac.uk/user/tong/gaugetheory/2ym.pdf|Yang Mills theory,]] by Professor David Tong, Trinity College, Cambridge university.

* //Note :// In year 2000, The Clay Mathematics Institute offered a $1 million prize for a full mathematical description. It remains unclaimed.