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| The laws of quantum
physics stand to the world of elementary particles in the way that
Newton's laws of classical mechanics stand to the macroscopic world.
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. 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. This property has been discovered
by physicists from experiment and confirmed by computer simulations,
but it still has not understood from a theoretical point of view.
Progress in establishing the existence of the Yang-Mills theory
and a mass gap and will require the introduction of fundamental
new ideas both in physics and in mathematics. |
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