Convergence of Dynamics on Inductive Systems of Banach Spaces

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...

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Bibliographic Details
Published in:Annales Henri Poincaré Vol. 25; no. 11; pp. 4931 - 4986
Main Authors: van Luijk, Lauritz, Stottmeister, Alexander, Werner, Reinhard F.
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 01.11.2024
Springer Nature B.V
Subjects:
Banach spaces
Classical and Quantum Gravitation
Classical mechanics
Convergence
Criteria
Dynamical Systems and Ergodic Theory
Elementary Particles
Mathematical and Computational Physics
Mathematical Methods in Physics
Phase transitions
Physics
Physics and Astronomy
Quantum Field Theory
Quantum Physics
Quantum theory
Relativity Theory
Theoretical
ISSN:1424-0637, 1424-0661
Online Access:Get full text
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Summary: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.
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ISSN:1424-0637
1424-0661
DOI:10.1007/s00023-024-01413-6