Singular Traces
Singular Traces

Author: Steven Lord

Publisher: Walter de Gruyter

Published: 2012-12-19

Total Pages: 468

ISBN-13: 311026255X

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This book is the first complete study and monograph dedicated to singular traces. The text mathematically formalises the study of traces in a self contained theory of functional analysis. Extensive notes will treat the historical development. The final section will contain the most complete and concise treatment known of the integration half of Connes' quantum calculus. Singular traces are traces on ideals of compact operators that vanish on the subideal of finite rank operators. Singular traces feature in A. Connes' interpretation of noncommutative residues. Particularly the Dixmier trace,which generalises the restricted Adler-Manin-Wodzicki residue of pseudo-differential operators and plays the role of the residue for a new catalogue of 'geometric' spaces, including Connes-Chamseddine standard models, Yang-Mills action for quantum differential forms, fractals, isospectral deformations, foliations and noncommutative index theory. The theory of singular traces has been studied after Connes' application to non-commutative geometry and physics by various authors. Recent work by Nigel Kalton and the authors has advanced the theory of singular traces.Singular traces can be equated to symmetric functionals of symmetric sequence or function spaces, residues of zeta functions and heat kernel asymptotics, and characterised by Lidksii and Fredholm formulas. The traces and formulas used in noncommutative geometry are now completely understood in this theory, with surprising new mathematical and physical consequences. For mathematical readers the text offers fundamental functional analysis results and, due to Nigel Kalton's contribution, a now complete theory of traces on compact operators. For mathematical physicists and other users of Connes' noncommutative geometry the text offers a complete reference to Dixmier traces and access to the deeper mathematical features of traces on ideals associated to the harmonic sequence. These features, not known and not discussed in general texts on noncommutative geometry, are undoubtably physical and probe to the fascinating heart of classical limits and quantization.

Theory
Theory

Author: Steven Lord

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2021-07-19

Total Pages: 416

ISBN-13: 3110378051

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This book is the second edition of the first complete study and monograph dedicated to singular traces. The text offers, due to the contributions of Albrecht Pietsch and Nigel Kalton, a complete theory of traces and their spectral properties on ideals of compact operators on a separable Hilbert space. The second edition has been updated on the fundamental approach provided by Albrecht Pietsch. For mathematical physicists and other users of Connes’ noncommutative geometry the text offers a complete reference to traces on weak trace class operators, including Dixmier traces and associated formulas involving residues of spectral zeta functions and asymptotics of partition functions.

Theory
Theory

Author: Steven Lord

Publisher: de Gruyter

Published: 2021-08-09

Total Pages: 440

ISBN-13: 9783110377798

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The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 30 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob.

Operator Algebras and Quantum Field Theory
Operator Algebras and Quantum Field Theory

Author: Sergio Doplicher

Publisher:

Published: 1997

Total Pages: 704

ISBN-13:

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A collection of papers presented at a conference in Rome on operator algebras and quantum field theory. Invited contributions on noncommutative dynamical systems, the Baum-Cohnes and the Novikov conjecture, the Atiyah-Singer index theorem, and Banach Space aspects are included.

[Set Singular Traces, Volume 1+2]
[Set Singular Traces, Volume 1+2]

Author:

Publisher:

Published: 2023-05-22

Total Pages: 0

ISBN-13: 9783110703184

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This book is the second edition of the first complete study and monograph dedicated to singular traces. The first volume offers, due to the contributions of Albrecht Pietsch and Nigel Kalton, a complete theory of traces and their spectral properties on ideals of compact operators, updated in this second edition on the fundamental new approach for compact operators, the Pietsch correspondence. For mathematical physicists and other users of Connes' noncommutative geometry the text offers a complete reference to Dixmier traces and associated formulas involving residues of spectral zeta functions and asymptotics of partition functions. An operator based theory of pseudodifferential operators is used to detail the deep association between the noncommutative residue in differential geometry and singular traces. The second volume introduces noncommutative integration theory on semifinite von Neumann algebras and the theory of singular traces for symmetric operator spaces. Deeper aspects of the association between measurability, poles and residues of spectral zeta functions, and asymptotics of heat traces are studied. Applications in Connes' noncommutative geometry that are detailed include integration of quantum differentials, measures on fractals, and Connes' character formula concerning the Hochschild class of the Chern character.

The Greatest Works of French Literature (English Edition)
The Greatest Works of French Literature (English Edition)

Author: Charles Baudelaire

Publisher: e-artnow

Published: 2020-12-17

Total Pages: 22266

ISBN-13:

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This unique collection of the greatest French classics books has been designed and formatted to the highest digital standards: A History of French Literature François Rabelais: Gargantua and Pantagruel Molière: Tartuffe or the Hypocrite The Misanthrope The Miser The Imaginary Invalid The Impostures of Scapin… Jean Racine: Phaedra Pierre Corneille: The Cid Voltaire: Candide Zadig Micromegas The Huron A Philosophical Dictionary… Jean-Jacques Rousseau: Confessions Emile The Social Contract De Laclos: Dangerous Liaisons Stendhal

Revolutionary Hope After Nihilism
Revolutionary Hope After Nihilism

Author: Saladdin Ahmed

Publisher: Bloomsbury Publishing

Published: 2022-07-28

Total Pages: 265

ISBN-13: 135026931X

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As we face new and debilitating catastrophes caused by capitalism and nation-state politics, Saladdin Ahmed argues that our only hope is to create space for a new world by negating the existing order. To achieve this new society, Revolutionary Hope After Nihilism outlines a practical philosophy of change that rejects ideologies of false hope and passive hopelessness. Drawing public attention to the decisiveness of the present historical moment, Ahmed introduces a critical theory of social emancipation based on post-Soviet revolutionary movements that have emerged at the margins of the global social order. The rise of socially and politically exclusionary movements in multiple parts of the world, ongoing ecological crisis, anti-Black racism, and the concretization of despair brought about by the COVID-19 pandemic demand a new approach to revolution, which Ahmed argues, must be rooted in the experiences of the most oppressed in society. Realizing the epistemological potential of emancipatory movements, Ahmed rejects dystopian nihilism and positions our focus on marginalized spaces to break out of capitalist totalitarianism.