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Yang-Mills Existence and Mass Gap Problem

The Yang-Mills existence and mass gap problem asks for a mathematically rigorous construction of a nontrivial quantum Yang-Mills theory on R^4 with a positive mass gap, for every compact simple gauge group G (Jaffe and Witten). Here G is a compact Lie group with a simple Lie algebra. The construction must satisfy the axiomatic requirements of quantum field theory specified in the official problem description. A positive mass gap requires the energy operator spectrum above the vacuum to be bounded away from zero.

This is one of the Millennium Prize Problems and remains unsolved (Clay Mathematics Institute). The problem concerns the existence and properties of the quantum field theory, rather than merely finding solutions of the classical Yang-Mills equation.

See also

Mass Gap, Millennium Prize Problems, Quantum Field Theory, Yang-Mills Equation, Yang-Mills Theory

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References

Clay Mathematics Institute. "Yang-Mills & the Mass Gap." https://www.claymath.org/millennium/yang-mills-the-maths-gap/.Jaffe, A. and Witten, E. "Quantum Yang-Mills Theory." Clay Mathematics Institute. https://www.claymath.org/wp-content/uploads/2022/06/yangmills.pdf.

Cite this as:

Weisstein, Eric W. "Yang-Mills Existence and Mass Gap Problem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Yang-MillsExistenceandMassGapProblem.html

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