Singular Traces
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Trace Formulas
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Author : Steven Lord
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2023-04-03
Trace Formulas written by Steven Lord and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-03 with Mathematics categories.
This 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 Memory Trace Ple Memory
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Author : Erich Goldmeier
language : en
Publisher: Psychology Press
Release Date : 2014-05-09
The Memory Trace Ple Memory written by Erich Goldmeier and has been published by Psychology Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-09 with Psychology categories.
There was some agreement about what memory traces were not, but little about what actually did characterize the memory trace. Yet models and theories of memory at the time could not help making implicit and often unrecognized assumptions about the memory trace. Originally published in 1982, this title aimed to strengthen the meagre base on which memory theories rested at the time. It challenges old assumptions and introduces new concepts, foremost the notion of singularity, as they become necessary to understand traces adequately. Some research data of the past was found in need of reinterpretation. The result is a new theory of the memory trace.
Mathematical Physics In Mathematics And Physics
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Author : Roberto Longo
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
Mathematical Physics In Mathematics And Physics written by Roberto Longo and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
The beauty and the mystery surrounding the interplay between mathematics and physics is captured by E. Wigner's famous expression, ``The unreasonable effectiveness of mathematics''. We don't know why, but physical laws are described by mathematics, and good mathematics sooner or later finds applications in physics, often in a surprising way. In this sense, mathematical physics is a very old subject-as Egyptian, Phoenician, or Greek history tells us. But mathematical physics is a very modern subject, as any working mathematician or physicist can witness. It is a challenging discipline that has to provide results of interest for both mathematics and physics. Ideas and motivations from both these sciences give it a vitality and freshness that is difficult to find anywhere else. One of the big physical revolutions in the twentieth century, quantum physics, opened a new magnificent era for this interplay. With the appearance of noncommutative analysis, the role of classical calculus has been taken by commutation relations, a subject still growing in an astonishing way. A good example where mathematical physics showed its power, beauty, and interdisciplinary character is the Doplicher-Haag-Roberts analysis of superselection sectors in the late 1960s. Not only did this theory explain the origin of statistics and classify it, but year after year, new connections have merged, for example with Tomita-Takesaki modular theory, Jones theory of subfactors, and Doplicher-Roberts abstract duality for compact groups. This volume contains the proceedings of the conference, ``Mathematical Physics in Mathematics and Physics'', dedicated to Sergio Doplicher and John E. Roberts held in Siena, Italy. The articles offer current research in various fields of mathematical physics, primarily concerning quantum aspects of operator algebras.
Singular Traces
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Author : Steven Lord
language : en
Publisher: Walter de Gruyter
Release Date : 2012-12-19
Singular Traces written by Steven Lord and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-19 with Mathematics categories.
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
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Author : Steven Lord
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2021-07-19
Theory written by Steven Lord and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-19 with Mathematics categories.
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.
Noncommutative Geometry And The Standard Model Of Elementary Particle Physics
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Author : Florian Scheck
language : en
Publisher: Springer
Release Date : 2008-01-11
Noncommutative Geometry And The Standard Model Of Elementary Particle Physics written by Florian Scheck and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-11 with Science categories.
The outcome of a close collaboration between mathematicians and mathematical physicists, these lecture notes present the foundations of A. Connes noncommutative geometry as well as its applications in particular to the field of theoretical particle physics. The coherent and systematic approach makes this book useful for experienced researchers and postgraduate students alike.
Regularised Integrals Sums And Traces
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Author : Sylvie Paycha
language : en
Publisher: American Mathematical Soc.
Release Date : 2012
Regularised Integrals Sums And Traces written by Sylvie Paycha and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
``Regularization techniques'' is the common name for a variety of methods used to make sense of divergent series, divergent integrals, or traces of linear operators in infinite-dimensional spaces. Such methods are often indispensable in problems of number theory, geometry, quantum field theory, and other areas of mathematics and theoretical physics. However arbitrary and noncanonical they might seem at first glance, regularized sums, integrals, and traces often contain canonical concepts, and the main purpose of this book is to illustrate and explain this. This book provides a unified and self-contained mathematical treatment of various regularization techniques. The author shows how to derive regularized sums, integrals, and traces from certain canonical building blocks of the original divergent object. In the process of putting together these ``building blocks'', one encounters many problems and ambiguities caused by various so-called anomalies, which are investigated and explained in detail. Nevertheless, it turns out that the corresponding canonical sums, integrals, sums, and traces are well behaved, thus making the regularization procedure possible and manageable. This new unified outlook on regularization techniques in various fields of mathematics and in quantum field theory can serve as an introduction for anyone from a beginning mathematician interested in the subject to an experienced physicist who wants to gain a unified outlook on techniques he/she uses on a daily basis.
Geometric And Topological Methods For Quantum Field Theory
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Author : Alexander Cardona
language : en
Publisher: Cambridge University Press
Release Date : 2013-05-09
Geometric And Topological Methods For Quantum Field Theory written by Alexander Cardona and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-09 with Mathematics categories.
A unique presentation of modern geometric methods in quantum field theory for researchers and graduate students in mathematics and physics.
The Future Of Testimony
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Author : Antony Rowland
language : en
Publisher: Routledge
Release Date : 2014-06-20
The Future Of Testimony written by Antony Rowland and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-20 with Social Science categories.
Celebrating the twentieth anniversary of the groundbreaking Testimony, this collection brings together the leading academics from a range of scholarly fields to explore the meaning, use, and value of testimony in law and politics, its relationship to other forms of writing like literature and poetry, and its place in society. It visits testimony in relation to a range of critical developments, including the rise of Truth Commissions and the explosion and radical extension of human rights discourse; renewed cultural interest in perpetrators of violence alongside the phenomenal commercial success of victim testimony (in the form of misery memoirs); and the emergence of disciplinary interest in genocide, terror, and other violent atrocities. These issues are necessarily inflected by the question of witnessing violence, pain, and suffering at both the local and global level, across cultures, and in postcolonial contexts. At the volume’s core is an interdisciplinary concern over the current and future nature of witnessing as it plays out through a ‘new’ Europe, post-9/11 US, war-torn Africa, and in countless refugee and detention centers, and as it is worked out by lawyers, journalists, medics, and novelists. The collection draws together an international range of case-studies, including discussion of the former Yugoslavia, Gaza, and Rwanda, and encompasses a cross-disciplinary set of texts, novels, plays, testimonial writing, and hybrid testimonies. The volume situates itself at the cutting-edge of debate and as such brings together the leading thinkers in the field, requiring that each address the future, anticipating and setting the future terms of debate on the importance of testimony.
Trauma In Contemporary Literature
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Author : Marita Nadal
language : en
Publisher: Routledge
Release Date : 2014-03-26
Trauma In Contemporary Literature written by Marita Nadal and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-26 with Literary Criticism categories.
Trauma in Contemporary Literature analyzes contemporary narrative texts in English in the light of trauma theory, including essays by scholars of different countries who approach trauma from a variety of perspectives. The book analyzes and applies the most relevant concepts and themes discussed in trauma theory, such as the relationship between individual and collective trauma, historical trauma, absence vs. loss, the roles of perpetrator and victim, dissociation, nachträglichkeit, transgenerational trauma, the process of acting out and working through, introjection and incorporation, mourning and melancholia, the phantom and the crypt, postmemory and multidirectional memory, shame and the affects, and the power of resilience to overcome trauma. Significantly, the essays not only focus on the phenomenon of trauma and its diverse manifestations but, above all, consider the elements that challenge the aporias of trauma, the traps of stasis and repetition, in order to reach beyond the confines of the traumatic condition and explore the possibilities of survival, healing and recovery.