What is the Yang-Mills millennium problem?
In: Physics
In Quantum Physics, particles sometimes behave as points, with a definite position, and other times spread out like waves. There are a number of theories around this phenomenon, including one named Yang-Mills. The problem with Yang-Mills is something called the “mass gap”. In classical theory, Y-M predicts particles that have no mass and long-range forces. The quantum theory of Y-M needs to match the real world, with short range forces and massive (as in having mass, not huge) particles.
In order to work out the quantum theory for Y-M, we basically need a new kind of math. We have some approximations and simplifications, but it’s kind of like knowing the simple form of the Pythagorean Theorem (a^(2) + b^(2) = c^(2)) without knowing Trigonometry. It’s great if all we have is right triangles, but once we get outside that, we don’t have the fundamental equations or knowledge of Sine, Cosine and Tangent to work out the general cases.
The Y-M Millennium problem is essentially developing that new branch of mathematics that works for Quantum Theory.
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