Convergence of Dynamics on Inductive Systems of Banach Spaces

Fuente: arXiv
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Autores principales: van Luijk, Lauritz, Stottmeister, Alexander, Werner, Reinhard F.
Formato: Preprint
Publicado: 2023
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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