Yang–Mills and Mass Gap problem

 

The Yang-Mills existence and mass gap problem is one of the most important and challenging unsolved problems in theoretical physics. It relates to the behavior of quantum chromodynamics, the theory that describes the strong nuclear force that binds protons and neutrons together in the atomic nucleus.

The problem can be stated as follows: Does a quantum Yang-Mills theory with a non-zero coupling constant exist in four spacetime dimensions, and if so, does it have a mass gap? A mass gap refers to the existence of a positive lower bound on the masses of the particles that can appear in the theory.

Despite much effort, this problem remains unsolved. It is one of the seven Millennium Prize Problems identified by the Clay Mathematics Institute, with a one million dollar prize for its solution.

Several approaches have been taken to address the Yang-Mills and mass gap problem, including lattice simulations, functional methods, and perturbative expansions. Progress has been made in understanding the problem in the context of supersymmetric theories and in low-dimensional models, but a complete solution remains elusive.

In recent years, there has been renewed interest in the problem, with new ideas and techniques being developed to tackle it. While a complete solution may still be some way off, progress in this area has the potential to revolutionize our understanding of the fundamental forces of nature.