Differential Algebraic Framework for Quantum Chromodynamics: A Constructive Approach to Non-Perturbative QCD
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| Format: | Recurso digital |
| Langue: | anglais |
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Zenodo
2026
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| _version_ | 1866901338257883136 |
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| author | liu, shifa |
| author_facet | liu, shifa |
| contents | <p>This paper develops a comprehensive differential algebraic framework for constructing explicit solutions to Quantum Chromodynamics (QCD) field equations.Building on the theory of differential algebraic closures and geometric PDE methods, we construct explicit representations for gauge fields, quark fields, and gauge invariant observables within appropriately defined differential closures. The key innovation is the systematic incorporation of gauge symmetry, renormalization group flow, and non-perturbative effects through recursive adjunction processes.We provide detailed constructions including instantons and Wilson loops with complete verifications, and establish precise connections with classical QCD theory. The framework offers new computational tools for non-perturbative QCD while maintaining mathematical rigor. Our approach carefully addresses the technical conditions required for the existence of representations, particularly gauge invariance, renormalization, and convergence properties in differential algebraic extensions.A significant contribution is the proof that the full instanton moduli space admits explicit representation within the differential closure, enabling constructive computation of topological effects. We also provide algorithms for verifying these conditions and computing the field configurations with certified error bounds. The framework enables new predictions for confinement scaling behavior and chiral symmetry breaking patterns.Enhanced Mathematical Foundation: We establish precise connections to the model theory of differentially closed fields, clarifying the logical foundations of our constructions. The framework is further strengthened through a comprehensive treatment of distribution-valued solutions via Colombeau-type algebras and Sobolev completions, ensuring rigorous handling of quantum fields as operator valued distributions.Modern Physical Connections: Our approach incorporates contemporary understanding of the gluon mass gap via the Schwinger mechanism, provides a constructive realization of the dual superconductor confinement picture, and implements modern precision constraints from hadronic spectroscopy and CP-violation experiments. The computational framework is designed to be compatible with emerging quantum computing paradigms for lattice field theories.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18163233 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Differential Algebraic Framework for Quantum Chromodynamics: A Constructive Approach to Non-Perturbative QCD liu, shifa Quantum Chromodynamics, Differential algebra, Gauge theory, Non-perturbative methods, Yang-Mills equations, Renormalization group, Instan tons, Wilson loops, Constructive field theory, Topological charge, Chiral symmetry breaking, Gluon mass gap, Entanglement entropy, Strong CP problem, Differen tially closed fields, Colombeau algebras, Hopf algebra renormalization <p>This paper develops a comprehensive differential algebraic framework for constructing explicit solutions to Quantum Chromodynamics (QCD) field equations.Building on the theory of differential algebraic closures and geometric PDE methods, we construct explicit representations for gauge fields, quark fields, and gauge invariant observables within appropriately defined differential closures. The key innovation is the systematic incorporation of gauge symmetry, renormalization group flow, and non-perturbative effects through recursive adjunction processes.We provide detailed constructions including instantons and Wilson loops with complete verifications, and establish precise connections with classical QCD theory. The framework offers new computational tools for non-perturbative QCD while maintaining mathematical rigor. Our approach carefully addresses the technical conditions required for the existence of representations, particularly gauge invariance, renormalization, and convergence properties in differential algebraic extensions.A significant contribution is the proof that the full instanton moduli space admits explicit representation within the differential closure, enabling constructive computation of topological effects. We also provide algorithms for verifying these conditions and computing the field configurations with certified error bounds. The framework enables new predictions for confinement scaling behavior and chiral symmetry breaking patterns.Enhanced Mathematical Foundation: We establish precise connections to the model theory of differentially closed fields, clarifying the logical foundations of our constructions. The framework is further strengthened through a comprehensive treatment of distribution-valued solutions via Colombeau-type algebras and Sobolev completions, ensuring rigorous handling of quantum fields as operator valued distributions.Modern Physical Connections: Our approach incorporates contemporary understanding of the gluon mass gap via the Schwinger mechanism, provides a constructive realization of the dual superconductor confinement picture, and implements modern precision constraints from hadronic spectroscopy and CP-violation experiments. The computational framework is designed to be compatible with emerging quantum computing paradigms for lattice field theories.</p> |
| title | Differential Algebraic Framework for Quantum Chromodynamics: A Constructive Approach to Non-Perturbative QCD |
| topic | Quantum Chromodynamics, Differential algebra, Gauge theory, Non-perturbative methods, Yang-Mills equations, Renormalization group, Instan tons, Wilson loops, Constructive field theory, Topological charge, Chiral symmetry breaking, Gluon mass gap, Entanglement entropy, Strong CP problem, Differen tially closed fields, Colombeau algebras, Hopf algebra renormalization |
| url | https://doi.org/10.5281/zenodo.18163233 |