The Well-Defined Path Integral: How the UCM Substrate Resolves Five Foundational Problems of Quantum Field Theory (UCM Paper 54)

Key Points

• This research aims to address five core mathematical problems in quantum field theory through the UCM substrate.
• Introduced the UCM substrate and its fibre-bundle structure.
• Analyzed how the bulk field contributes a finite Lebesgue measure.
• Evaluated the gauge field's contribution of a finite Haar measure.
• Eliminated the matter integral through gauge-matter unity.
• Constructed a complete partition function using well-defined measures.
• The UCM substrate resolves the issue of measure existence in infinite dimensions.
• Convergence of the Lorentzian integrand is achieved in this framework.
• Demonstrated that traditional issues with 4D Yang-Mills can be addressed.
• Validated Haag's theorem interactions within the UCM context.
• The complete partition function is now a finite product of well-defined measures.

Abstract