Yang–Mills existence and mass gap problem
E173924
The Yang–Mills existence and mass gap problem is a fundamental unsolved question in mathematical physics that asks for a rigorous proof that quantum Yang–Mills theory exists and exhibits a positive mass gap, and is one of the seven Millennium Prize Problems.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Yang–Mills existence and mass gap problem canonical | 2 |
| Jaffe–Witten problem statement | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T1523325 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Yang–Mills existence and mass gap problem Context triple: [Millennium Prize Problem, hasProblem, Yang–Mills existence and mass gap problem]
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A.
Millennium Prize Problem
The Millennium Prize Problem is one of seven famous unsolved mathematical problems designated by the Clay Mathematics Institute, each carrying a $1 million reward for a correct solution.
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B.
Poincaré conjecture
The Poincaré conjecture is a landmark problem in topology that characterizes the three-dimensional sphere among three-dimensional manifolds and was famously solved by Grigori Perelman in the early 2000s.
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C.
Atiyah–Singer index theorem
The Atiyah–Singer index theorem is a fundamental result in mathematics that links the analytical properties of elliptic differential operators to topological invariants of manifolds, unifying analysis, topology, and geometry.
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D.
Hilbert problems
The Hilbert problems are a famous list of 23 unsolved mathematical problems presented by David Hilbert in 1900 that profoundly influenced the development of 20th-century mathematics.
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E.
P versus NP problem
The P versus NP problem is a central unsolved question in theoretical computer science that asks whether every problem whose solution can be quickly verified by a computer can also be quickly solved by a computer.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Yang–Mills existence and mass gap problem Target entity description: The Yang–Mills existence and mass gap problem is a fundamental unsolved question in mathematical physics that asks for a rigorous proof that quantum Yang–Mills theory exists and exhibits a positive mass gap, and is one of the seven Millennium Prize Problems.
-
A.
Millennium Prize Problem
The Millennium Prize Problem is one of seven famous unsolved mathematical problems designated by the Clay Mathematics Institute, each carrying a $1 million reward for a correct solution.
-
B.
Poincaré conjecture
The Poincaré conjecture is a landmark problem in topology that characterizes the three-dimensional sphere among three-dimensional manifolds and was famously solved by Grigori Perelman in the early 2000s.
-
C.
Atiyah–Singer index theorem
The Atiyah–Singer index theorem is a fundamental result in mathematics that links the analytical properties of elliptic differential operators to topological invariants of manifolds, unifying analysis, topology, and geometry.
-
D.
Hilbert problems
The Hilbert problems are a famous list of 23 unsolved mathematical problems presented by David Hilbert in 1900 that profoundly influenced the development of 20th-century mathematics.
-
E.
P versus NP problem
The P versus NP problem is a central unsolved question in theoretical computer science that asks whether every problem whose solution can be quickly verified by a computer can also be quickly solved by a computer.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
Millennium Prize Problem
ⓘ
open problem in mathematical physics ⓘ |
| asksFor |
proof of existence of a nontrivial quantum Yang–Mills theory with compact simple gauge group
ⓘ
proof of existence of a positive mass gap ⓘ proof that the least nonzero energy of an excitation above the vacuum is strictly positive ⓘ proof that the theory satisfies the standard axioms of quantum field theory ⓘ rigorous construction of quantum Yang–Mills theory on four-dimensional Minkowski space ⓘ |
| concerns |
Yang–Mills theory
ⓘ
existence of quantum Yang–Mills theory ⓘ mass gap in quantum Yang–Mills theory ⓘ |
| difficulty | very hard ⓘ |
| dimension | 4-dimensional spacetime ⓘ |
| field |
mathematical physics
ⓘ
mathematics ⓘ quantum field theory ⓘ theoretical physics ⓘ |
| formalizedBy |
Jaffe–Witten problem statement
ⓘ
linked to:
Yang–Mills existence and mass gap problem
|
| hasConsequence |
insight into strong coupling behavior of quantum fields
ⓘ
mathematical understanding of confinement in QCD ⓘ rigorous foundation for non-abelian gauge theories ⓘ |
| hasNoKnown | complete rigorous solution ⓘ |
| hasPrize | US$1,000,000 ⓘ |
| involves |
Wightman axioms or Osterwalder–Schrader axioms
ⓘ
linked to:
Wightman axioms
existence of a vacuum state ⓘ local gauge invariance ⓘ non-abelian gauge symmetry ⓘ renormalization in quantum field theory ⓘ spectral properties of the Hamiltonian ⓘ |
| namedAfter | Yang–Mills theory ⓘ |
| partOf | list of seven Millennium Prize Problems ⓘ |
| relatedConcept |
lattice gauge theory
ⓘ
mass gap ⓘ nonperturbative quantum field theory ⓘ quantum chromodynamics ⓘ spectral gap ⓘ |
| relatedTo |
Clay Millennium Prize Problems
ⓘ
linked to:
Millennium Prize Problem
confinement in quantum chromodynamics ⓘ non-abelian gauge theories ⓘ |
| requires |
compact simple gauge group such as SU(3)
ⓘ
nontrivial quantum field theory distinct from the free theory ⓘ |
| requiresProofIn |
Minkowski spacetime
ⓘ
linked to:
Minkowski space-time
four-dimensional Euclidean space (via Wick rotation) ⓘ |
| sponsor | Clay Mathematics Institute ⓘ |
| status | unsolved ⓘ |
| typicalGaugeGroup |
SU(2)
ⓘ
linked to:
rotation group SU(2)
SU(3) ⓘ SU(N) ⓘ
linked to:
special unitary group SU(n)
|
| yearProposed | 2000 ⓘ |
How these facts were elicited
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Instruction
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Input
Subject: Yang–Mills existence and mass gap problem Description of subject: The Yang–Mills existence and mass gap problem is a fundamental unsolved question in mathematical physics that asks for a rigorous proof that quantum Yang–Mills theory exists and exhibits a positive mass gap, and is one of the seven Millennium Prize Problems.
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Yang–Mills existence and mass gap problem