Sobolev Norm Boundedness Estimates for the Dynamic Group Law of Chronogroups
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2025
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| _version_ | 1866902278828457984 |
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| author | zhou, Changzheng ZHOU, ziqing |
| author_facet | zhou, Changzheng ZHOU, ziqing |
| contents | <p>This paper establishes a boundedness theorem for Sobolev norms of a class of non<br>commutative associative operations originating from physical systems. By axiomati<br>cally defining a ”chronogroup” structure with time evolution parameters, the problem<br> of Sobolev norm estimation for its dynamic group law ∗t is decomposed into controlling<br> the classical Lie group multiplication term and the gauge phase correction term. The<br> core proof combines spectral cohomology theory describing energy-scale phase transition<br> behavior in gauge fields with generalized Harish-Chandra estimates, demonstrating that<br> for any Sobolev exponent s > 0, there exists a constant Cs such that g ∗t hHs ≤<br> Cs g Hs hHs. This result provides a rigorous mathematical foundation for operator<br> functional analysis in non-perturbative quantum field theory</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_16990576 |
| institution | Zenodo |
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| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Sobolev Norm Boundedness Estimates for the Dynamic Group Law of Chronogroups zhou, Changzheng ZHOU, ziqing Chronogroup; dynamic group law; Sobolev space; norm estimation; spectral cohomology <p>This paper establishes a boundedness theorem for Sobolev norms of a class of non<br>commutative associative operations originating from physical systems. By axiomati<br>cally defining a ”chronogroup” structure with time evolution parameters, the problem<br> of Sobolev norm estimation for its dynamic group law ∗t is decomposed into controlling<br> the classical Lie group multiplication term and the gauge phase correction term. The<br> core proof combines spectral cohomology theory describing energy-scale phase transition<br> behavior in gauge fields with generalized Harish-Chandra estimates, demonstrating that<br> for any Sobolev exponent s > 0, there exists a constant Cs such that g ∗t hHs ≤<br> Cs g Hs hHs. This result provides a rigorous mathematical foundation for operator<br> functional analysis in non-perturbative quantum field theory</p> |
| title | Sobolev Norm Boundedness Estimates for the Dynamic Group Law of Chronogroups |
| topic | Chronogroup; dynamic group law; Sobolev space; norm estimation; spectral cohomology |
| url | https://doi.org/10.5281/zenodo.16990576 |