What is the Yang Mills and mass gap problem?

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. …

Who Solved Yang Mills and Mass Gap?

Russian mathematician Grigori Perelman was awarded the Prize on March 18 last year for solving one of the problems, the Poincaré conjecture—as yet the only problem that’s been solved. Famously, he turned down the $1,000,000 Millennium Prize.

How important is Yang Mills theory?

One of the most important results obtained for Yang–Mills theory is asymptotic freedom. This result can be obtained by assuming that the coupling constant g is small (so small nonlinearities), as for high energies, and applying perturbation theory.

Is Yang Mills theory solved?

Yang–Mills theory exists and satisfies the standard of rigor that characterizes contemporary mathematical physics, in particular constructive quantum field theory, and. The mass of the least massive particle of the force field predicted by the theory is strictly positive.

Is Yang-Mills theory correct?

The current state of Yang-Mills theory has been compared to the early days of the calculus, when undeniably accurate and useful results were being obtained but before the formal development of analysis added rigorous definitions that eliminated logical fallacies.

What is Yang-Mills field?

Yang–Mills fields, which are also called gauge fields, are used in modern physics to describe physical fields that play the role of carriers of an interaction.

What is the Yang-Mills existence and mass gap problem?

In mathematical physics, the Yang–Mills existence and mass gap problem is an unsolved problem and one of the seven Millennium Prize Problems defined by the Clay Mathematics Institute, which has offered a prize of US$1,000,000 to the one who solves it. The problem is phrased as follows:

What is quantquantum Yang-Mills theory?

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.

What is the mass gap in quantum field theory?

In quantum field theory, the mass gap is the difference in energy between the vacuum and the next lowest energy state. The energy of the vacuum is zero by definition, and assuming that all energy states can be thought of as particles in plane-waves, the mass gap is the mass of the lightest particle.

Is the mass gap real or just a myth?

The evidence that the mass gap is real comes from renormalization group calculations of the strength of various interactions; simulations in lattice QCD; and, among other approaches, the most modern tools are based on the holographic AdS/CFT correspondence.