Details
| Original language | English |
|---|---|
| Publication status | E-pub ahead of print - 28 Jun 2023 |
Abstract
Keywords
- math-ph, math.MP, math.OA, quant-ph
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2023.
Research output: Working paper/Preprint › Preprint
}
TY - UNPB
T1 - Convergence of Dynamics on Inductive Systems of Banach Spaces
AU - van Luijk, Lauritz
AU - Stottmeister, Alexander
AU - Werner, Reinhard F.
N1 - Comments welcome
PY - 2023/6/28
Y1 - 2023/6/28
N2 - 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.
AB - 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.
KW - math-ph
KW - math.MP
KW - math.OA
KW - quant-ph
M3 - Preprint
BT - Convergence of Dynamics on Inductive Systems of Banach Spaces
ER -