Causal Nets of Operator Algebras

Causal Nets of Operator Algebras
Author: Hellmut Baumgärtel
Publisher: De Gruyter Akademie Forschung
Total Pages: 488
Release: 1992
Genre: Mathematical physics
ISBN:

For advanced students in mathematics and mathematicians, as well as theoretical physicists, this volume presents the theory of nets of operator algebras, in particular nets connected with a causality condition. Such nets appear in mathematical formulations of quantum statistical mechanics and of quantum field theory. In this volume, the emphasis lies on nets which are linked with the algebraic approach to quantum field theory. Assumes a basic knowledge of functional analysis, in particular in the field of operator algebras. Annotation copyright by Book News, Inc., Portland, OR

Aspects of Operator Algebras and Applications

Aspects of Operator Algebras and Applications
Author: Ara, Pere
Publisher: American Mathematical Soc.
Total Pages: 178
Release: 2011
Genre: Mathematics
ISBN: 0821849050

The contents of this book cover K-theory for operator algebras, modular theory by example, modular theory for the Von Neumann algebras of local quantum physics, and much more.

C*-Algebras and Operator Theory

C*-Algebras and Operator Theory
Author: Gerald J. Murphy
Publisher: Academic Press
Total Pages: 297
Release: 2014-06-28
Genre: Mathematics
ISBN: 0080924964

This book constitutes a first- or second-year graduate course in operator theory. It is a field that has great importance for other areas of mathematics and physics, such as algebraic topology, differential geometry, and quantum mechanics. It assumes a basic knowledge in functional analysis but no prior acquaintance with operator theory is required.

Mathematical Theory of Quantum Fields

Mathematical Theory of Quantum Fields
Author: Huzihiro Araki
Publisher: Oxford University Press, USA
Total Pages: 254
Release: 1999
Genre: Mathematics
ISBN: 9780198517733

Quantum field theory is an area of wide and growing interest to students and researchers of both mathematics and physics. This text is an introduction to the subject which uses mathematical theory of operator algebras to present the theory.

The Ultimate Constituents of the Material World

The Ultimate Constituents of the Material World
Author: Meinard Kuhlmann
Publisher: Walter de Gruyter
Total Pages: 291
Release: 2013-05-02
Genre: Philosophy
ISBN: 3110326124

Today, quantum field theory (QFT)—the mathematical and conceptual framework for contemporary elementary particle physics—is the best starting point for analysing the fundamental building blocks of the material world. QFT if taken seriously in its metaphysical implications yields a picture of the world that is at variance with central classical conceptions. The core of Kuhlmann’s investigation consists in the analysis of various ontological interpretations of QFT, e.g. substance ontologies as well as a process-ontological approach. Eventually, Kuhlmann proposes a dispositional trope ontology, according to which particularized properties and not things are the most basic entities, in terms of which all other entities are to be analysed, e.g as bundles of properties. This book was chosen for the 2009 ontos-Award for research on analytical ontology and metaphysics by the German Society for Analytical Philosophy.

Quantum Field Theory I: Basics in Mathematics and Physics

Quantum Field Theory I: Basics in Mathematics and Physics
Author: Eberhard Zeidler
Publisher: Springer Science & Business Media
Total Pages: 1060
Release: 2007-04-18
Genre: Science
ISBN: 354034764X

This is the first volume of a modern introduction to quantum field theory which addresses both mathematicians and physicists, at levels ranging from advanced undergraduate students to professional scientists. The book bridges the acknowledged gap between the different languages used by mathematicians and physicists. For students of mathematics the author shows that detailed knowledge of the physical background helps to motivate the mathematical subjects and to discover interesting interrelationships between quite different mathematical topics. For students of physics, fairly advanced mathematics is presented, which goes beyond the usual curriculum in physics.

Local Quantum Physics

Local Quantum Physics
Author: Rudolf Haag
Publisher: Springer Science & Business Media
Total Pages: 400
Release: 2012-12-06
Genre: Science
ISBN: 3642614582

The new edition provided the opportunity of adding a new chapter entitled "Principles and Lessons of Quantum Physics". It was a tempting challenge to try to sharpen the points at issue in the long lasting debate on the Copenhagen Spirit, to assess the significance of various arguments from our present vantage point, seventy years after the advent of quantum theory, where, after ali, some problems appear in a different light. It includes a section on the assumptions leading to the specific mathematical formalism of quantum theory and a section entitled "The evolutionary picture" describing my personal conclusions. Alto gether the discussion suggests that the conventional language is too narrow and that neither the mathematical nor the conceptual structure are built for eter nity. Future theories will demand radical changes though not in the direction of a return to determinism. Essential lessons taught by Bohr will persist. This chapter is essentially self-contained. Some new material has been added in the last chapter. It concerns the char acterization of specific theories within the general frame and recent progress in quantum field theory on curved space-time manifolds. A few pages on renor malization have been added in Chapter II and some effort has been invested in the search for mistakes and unclear passages in the first edition. The central objective of the book, expressed in the title "Local Quantum Physics", is the synthesis between special relativity and quantum theory to gether with a few other principles of general nature.

Perturbative Algebraic Quantum Field Theory

Perturbative Algebraic Quantum Field Theory
Author: Kasia Rejzner
Publisher: Springer
Total Pages: 186
Release: 2016-03-16
Genre: Science
ISBN: 3319259016

Perturbative Algebraic Quantum Field Theory (pAQFT), the subject of this book, is a complete and mathematically rigorous treatment of perturbative quantum field theory (pQFT) that doesn’t require the use of divergent quantities and works on a large class of Lorenzian manifolds. We discuss in detail the examples of scalar fields, gauge theories and the effective quantum gravity. pQFT models describe a wide range of physical phenomena and have remarkable agreement with experimental results. Despite this success, the theory suffers from many conceptual problems. pAQFT is a good candidate to solve many, if not all, of these conceptual problems. Chapters 1-3 provide some background in mathematics and physics. Chapter 4 concerns classical theory of the scalar field, which is subsequently quantized in chapters 5 and 6. Chapter 7 covers gauge theory and chapter 8 discusses effective quantum gravity. The book aims to be accessible to researchers and graduate students, who are interested in the mathematical foundations of pQFT.

Advances in Algebraic Quantum Field Theory

Advances in Algebraic Quantum Field Theory
Author: Romeo Brunetti
Publisher: Springer
Total Pages: 460
Release: 2015-09-04
Genre: Science
ISBN: 3319213539

This text focuses on the algebraic formulation of quantum field theory, from the introductory aspects to the applications to concrete problems of physical interest. The book is divided in thematic chapters covering both introductory and more advanced topics. These include the algebraic, perturbative approach to interacting quantum field theories, algebraic quantum field theory on curved spacetimes (from its structural aspects to the applications in cosmology and to the role of quantum spacetimes), algebraic conformal field theory, the Kitaev's quantum double model from the point of view of local quantum physics and constructive aspects in relation to integrable models and deformation techniques. The book is addressed to master and graduate students both in mathematics and in physics, who are interested in learning the structural aspects and the applications of algebraic quantum field theory.

Quantum Entanglements

Quantum Entanglements
Author: Rob Clifton
Publisher: Clarendon Press
Total Pages: 504
Release: 2004-09-23
Genre: Science
ISBN: 0191556491

Rob Clifton was one of the most brilliant and productive researchers in the foundations and philosophy of quantum theory; he died tragically at the age of 38. Jeremy Butterfield and Hans Halvorson present fourteen of his finest papers, all of which combine exciting philosophical discussion with rigorous mathematical results. Many of these papers break wholly new ground, either conceptually or technically. Others resolve a vague controversy into a precise technical problem, which is then solved; still others solve an open problem that had been in the air for some time. All of them show scientific and philosophical creativity of a high order, genuinely among the very best work in the field. The papers are grouped into four parts. First come four papers about the modal interpretation of quantum mechanics. Part II comprises three papers on the foundations of algebraic quantum field theory, with an emphasis on entanglement and nonlocality. The two papers in Part III concern the concept of a particle in relativistic quantum theories. One paper analyses localization; the other analyses the Unruh effect (Rindler quanta) using the algebraic approach to quantum theory. Finally, Part IV contains striking new results about such central issues as complementarity, Bohr's reply to the EPR argument, and no hidden variables theorems; and ends with a philosophical survey of the field of quantum information. The volume includes a full bibliography of Clifton's publications. Quantum Entanglements offers inspiration and substantial reward to graduates and professionals in the foundations of physics, with a background in philosophy, physics, or mathematics.