Convergence of Dynamics on Inductive Systems of Banach Spaces
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866929243880947712 |
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| author | van Luijk, Lauritz Stottmeister, Alexander Werner, Reinhard F. |
| author_facet | van Luijk, Lauritz Stottmeister, Alexander Werner, Reinhard F. |
| contents | Many features of physical systems, both qualitative and quantitative, become sharply defined or tractable only in some limiting situation. Examples are phase transitions in the thermodynamic limit, the emergence of classical mechanics from quantum theory at large action, and continuum quantum field theory arising from renormalization group fixed points. It would seem that few methods can be useful in such diverse applications. However, we here present a flexible modeling tool for the limit of theories: soft inductive limits constituting a generalization of inductive limits of Banach spaces. In this context, general criteria for the convergence of dynamics will be formulated, and these criteria will be shown to apply in the situations mentioned and more. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_16063 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Convergence of Dynamics on Inductive Systems of Banach Spaces van Luijk, Lauritz Stottmeister, Alexander Werner, Reinhard F. Mathematical Physics Operator Algebras Quantum Physics Many features of physical systems, both qualitative and quantitative, become sharply defined or tractable only in some limiting situation. Examples are phase transitions in the thermodynamic limit, the emergence of classical mechanics from quantum theory at large action, and continuum quantum field theory arising from renormalization group fixed points. It would seem that few methods can be useful in such diverse applications. However, we here present a flexible modeling tool for the limit of theories: soft inductive limits constituting a generalization of inductive limits of Banach spaces. In this context, general criteria for the convergence of dynamics will be formulated, and these criteria will be shown to apply in the situations mentioned and more. |
| title | Convergence of Dynamics on Inductive Systems of Banach Spaces |
| topic | Mathematical Physics Operator Algebras Quantum Physics |
| url | https://arxiv.org/abs/2306.16063 |