What does this research mean for the field?

A nontrivial pure Yang-Mills Wightman quantum field theory on R4 with a unique invariant vacuum and a strictly positive Hamiltonian mass gap exists for every compact connected non-abelian gauge group with simple Lie algebra. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To mathematically construct a four-dimensional pure Yang–Mills Wightman quantum field theory and rigorously prove the existence of a positive Hamiltonian mass gap for any compact connected gauge group with a simple Lie algebra.

August 24, 2026Open Access

Four-Dimensional Pure Yang–Mills Theory: Wightman Construction and Mass Gap for Compact Connected Gauge Groups with Simple Lie Algebra

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Authors

LPLeslie P. Polzer

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Implication

Theoretical analysis demonstrates the existence of a Wightman quantum field theory and a positive mass gap in four-dimensional pure Yang–Mills systems, indicating a proof of the Jaffe–Witten problem.

Key Points

To mathematically construct a four-dimensional pure Yang–Mills Wightman quantum field theory and rigorously prove the existence of a positive Hamiltonian mass gap for any compact connected gauge group with a simple Lie algebra.
Defined an intrinsic finite-law family for each global form using a faithful deployed Wilson representation.
Constructed the asymptotically free running coordinate and positive dimensional-transmutation scale via response-inverted flow.
Applied a cofinal finite-law catalog for Osterwalder–Schrader reconstruction and utilized a canonical Wilson-jet compiler to establish exact Callan–Symanzik transport and operator product expansion bounds.
Constructed an unconditional, nontrivial pure Yang–Mills Wightman quantum field theory on four-dimensional spacetime with a unique invariant vacuum state.
Proved the existence of a strictly positive Hamiltonian mass gap on the entire vacuum complement for all specified compact connected gauge groups.

Cite This Study

Leslie P. Polzer (2026) studied this question.

synapsesocial.com/papers/6a8c009fbca056c88e6df78d https://doi.org/10.5281/zenodo.22055692

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Four-Dimensional Pure Yang–Mills Theory: Wightman Construction and Mass Gap for Compact Connected Gauge Groups with Simple Lie Algebra

Discussion

Member takes

Implication

Key Points

Cite This Study

Four-Dimensional Pure Yang–Mills Theory: Wightman Construction and Mass Gap for Compact Connected Gauge Groups with Simple Lie Algebra

Discussion

Member takes

Implication

Key Points

Cite This Study

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