We propose a concrete mechanism linking the gluon condensate to the Yang-Mills mass gap. We invite mathematical physicists to help formulate this within rigorous constructive field theory.
This work proposes a physical mechanism for the Yang-Mills mass gap based on persistent vacuum strain induced by the gluon condensate. The approach uses a Hubbard-Stratonovich transformation to introduce an effective scalar field φ ~ Tr(F_μν F^μν), with the nonvanishing gluon condensate acting as a source term that prevents restoration of the symmetric vacuum.
While the phenomenological results match lattice QCD data remarkably well (m_gap = 1.65 ± 0.15 GeV vs. lattice 1.71 ± 0.05 GeV), the mathematical formalization requires expertise in constructive field theory, functional analysis, and rigorous QCD.
Uses O(x) = Tr(F_μν F^μν), a manifestly gauge-invariant composite operator, avoiding gauge-fixing complications.
Focuses directly on the correlator ⟨O(x)O(0)⟩ that the Clay Millennium Problem requires to be controlled.
Converts the problem into analyzing an effective scalar measure with a source determined by the measured gluon condensate.
Sidesteps gauge fixing and complex topological arguments, focusing on the induced effective measure properties.
If the Yang-Mills vacuum satisfies ⟨O⟩ ≠ 0, then the effective measure obtained via the Hubbard-Stratonovich representation admits a nontrivial minimum φ₀ ≠ 0 such that the correlator ⟨O(x)O(0)⟩ must decay exponentially, implying a positive mass gap.
This reduces the mass gap question to showing that the condensate forces a nontrivial minimum in the effective action for the composite field φ, and that this minimum controls the large-distance decay of the correlator.
Expertise in constructive field theory, functional analysis, or rigorous QCD. Experience with Hubbard-Stratonovich transformations, effective field theory, or lattice gauge theory.
We welcome feedback on whether this direction could be formulated rigorously, suggestions for mathematical tools that might help, and collaboration on developing the formal framework.
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