Differential Algebraic Methods in Twistor Theory: A Constructive Framework for Explicit Parameterizations and Geometric PDEs
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| Natura: | Recurso digital |
| Lingua: | inglese |
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2026
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| _version_ | 1866901051318206464 |
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| author | liu, shifa |
| author_facet | liu, shifa |
| contents | <p>This paper develops a comprehensive differential algebraic framework for twistor theory, establishing rigorous constructive methods for the explicit solution of twistor-geometric partial differential equations.We define the twistor differential closure Ktw(T ) through a meticulous transfinite induction process that incorporates holomorphic sections, twistor connections, self-dual curvature forms, and Penrose transform data while preserving complex-geometric structures. We prove complete existence and uniqueness theorems for this closure and establish explicit local parameterization theorems for twistor spaces with combinatorial correction terms derived from holomorphic tangent cone geometry. Within this framework,we provide unified solution representations for fundamental twistor geometric PDEs—including the self-dual Yang-Mills equations, twistor Dirac equations, and Einstein self-duality equations—with certified convergence in appropriate Sobolev-type norms on complex manifolds. The computational framework features efficient algorithms with precise complexity analysis and rigorous validation using complex interval arithmetic. We develop extensions to quantized twistor spaces, supersymmetric twistor theory,and twistor-based geometric deep learning, establishing new connections between differential algebra,complex geometry, and mathematical physics while maintaining full mathematical rigor throughout.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18112919 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Differential Algebraic Methods in Twistor Theory: A Constructive Framework for Explicit Parameterizations and Geometric PDEs liu, shifa Twistor theory, Differential algebra, Geometric PDEs, Explicit parameterization, Self dual geometry, Holomorphic vector bundles, Penrose transform, Constructive mathematics, Complex interval arithmetic <p>This paper develops a comprehensive differential algebraic framework for twistor theory, establishing rigorous constructive methods for the explicit solution of twistor-geometric partial differential equations.We define the twistor differential closure Ktw(T ) through a meticulous transfinite induction process that incorporates holomorphic sections, twistor connections, self-dual curvature forms, and Penrose transform data while preserving complex-geometric structures. We prove complete existence and uniqueness theorems for this closure and establish explicit local parameterization theorems for twistor spaces with combinatorial correction terms derived from holomorphic tangent cone geometry. Within this framework,we provide unified solution representations for fundamental twistor geometric PDEs—including the self-dual Yang-Mills equations, twistor Dirac equations, and Einstein self-duality equations—with certified convergence in appropriate Sobolev-type norms on complex manifolds. The computational framework features efficient algorithms with precise complexity analysis and rigorous validation using complex interval arithmetic. We develop extensions to quantized twistor spaces, supersymmetric twistor theory,and twistor-based geometric deep learning, establishing new connections between differential algebra,complex geometry, and mathematical physics while maintaining full mathematical rigor throughout.</p> |
| title | Differential Algebraic Methods in Twistor Theory: A Constructive Framework for Explicit Parameterizations and Geometric PDEs |
| topic | Twistor theory, Differential algebra, Geometric PDEs, Explicit parameterization, Self dual geometry, Holomorphic vector bundles, Penrose transform, Constructive mathematics, Complex interval arithmetic |
| url | https://doi.org/10.5281/zenodo.18112919 |