Time automorphisms on \(C^*\)-algebras
type: Item
instance of: scholarly article
title: Time automorphisms on \(C^*\)-algebras
zbMATH Open document ID: 1330.81240
published in: Mathematics
publication date: 2016-01-12T00:00:00Z
review text: Summary: Applications of fractional time derivatives in physics and engineering require the existence of nontranslational time automorphisms on the appropriate algebra of observables. The existence of time automorphisms on commutative and noncommutative \(C^*\)-algebras for interacting many-body systems is investigated in this article. A mathematical framework is given to discuss local stationarity in time and the global existence of fractional and nonfractional time automorphisms. The results challenge the concept of time flow as a translation along the orbits and support a more general concept of time flow as a convolution along orbits. Implications for the distinction of reversible and irreversible dynamics are discussed. The generalized concept of time as a convolution reduces to the traditional concept of time translation in a special limit.
Mathematics Subject Classification ID: 81V70
Mathematics Subject Classification ID: 81R15
Mathematics Subject Classification ID: 26A33
Mathematics Subject Classification ID: 82C22
Mathematics Subject Classification ID: 82C35
Mathematics Subject Classification ID: 46L05
Mathematics Subject Classification ID: 46L60
Mathematics Subject Classification ID: 46L40
zbMATH DE Number: 6528842
zbMATH Keywords: fractional time derivatives
zbMATH Keywords: fractional time evolution
zbMATH Keywords: \(C^*\)-algebra
zbMATH Keywords: local stationarity
zbMATH Keywords: irreversibility problem
author: R. Hilfer
MaRDI profile type: Publication
full work available at URL: math3030626
OpenAlex ID: W1523232915
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DOI: 10.3390/MATH3030626
description: scientific article; zbMATH DE number 6528842