IGI as an Infrared Regulator for the Yang–Mills Mass Gap Problem

This research note introduces an IGI-inspired framework for addressing the Yang–Mills mass gap problem, one of the Clay Millennium Prize Problems. In the IGI model, the fundamental state is expressed as a complex amplitude Z = \sqrt{\rho}\, e^{i\theta}, where \rho represents energetic density (hardware/body) and \theta encodes the informational phase (software/psyche). We propose an additional informational tensor Q_{\mu\nu}[\rho], acting as a natural infrared regulator. By coupling this regulator to the Yang–Mills action in a gauge-invariant way, we show how one may obtain Osterwalder–Schrader positivity, exponential clustering of gauge-invariant correlators, and ultimately a strictly positive spectral gap. The IGI approach provides a conceptual and mathematical bridge between physics, information theory, and complex systems, suggesting a constructive path toward resolving the mass gap problem. Keywords Yang–Mills theory Mass gap problem Clay Millennium Problems Osterwalder–Schrader positivity Exponential clustering Informational tensor IGI framework Complex systems Quantum field theory