When is 4D-Yang-Mills-Theorie possible

July 26, 2026Open Access

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Key Points

This work aims to construct a pure quantum Yang-Mills theory and prove the existence and strict positivity of its mass gap.
Utilizes lattice regularization with Wilson lattice action and renormalization-group flow.
Applies Osterwalder-Schrader reconstruction to verify relativistic quantum field theory axioms.
Implements dimensional calibration against three-dimensional models and detailed analysis of input parameters.
Establishes the existence of a mass gap greater than zero (${\Delta} > 0$) under specific conditions.
Identifies three main components of the mass-gap problem: existence, value, and positivity.
Demonstrates that the physical mass gap corresponds to a pseudospectral gap rather than a simple eigenvalue gap.

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Investigates the existence and positivity of the mass gap in 4D Yang-Mills theory, suggesting new theoretical frameworks.

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Elias Oulad Brahim (2026) studied this question.

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