Tomita's Theory of Modular Hilbert Algebras and its Applications
| Author | : M. Takesaki |
| Publisher | : Springer |
| Total Pages | : 126 |
| Release | : 2006-11-15 |
| Genre | : Mathematics |
| ISBN | : 3540362673 |
Tomitas Theory Of Modular Hilbert Algebras
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Tomita's Lectures on Observable Algebras in Hilbert Space
| Author | : Atsushi Inoue |
| Publisher | : Springer Nature |
| Total Pages | : 197 |
| Release | : 2021-03-01 |
| Genre | : Mathematics |
| ISBN | : 3030688933 |
This book is devoted to the study of Tomita's observable algebras, their structure and applications. It begins by building the foundations of the theory of T*-algebras and CT*-algebras, presenting the major results and investigating the relationship between the operator and vector representations of a CT*-algebra. It is then shown via the representation theory of locally convex*-algebras that this theory includes Tomita–Takesaki theory as a special case; every observable algebra can be regarded as an operator algebra on a Pontryagin space with codimension 1. All of the results are proved in detail and the basic theory of operator algebras on Hilbert space is summarized in an appendix. The theory of CT*-algebras has connections with many other branches of functional analysis and with quantum mechanics. The aim of this book is to make Tomita’s theory available to a wider audience, with the hope that it will be used by operator algebraists and researchers in these related fields.
Perspectives on Noncommutative Geometry
| Author | : Masoud Khalkhali |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 176 |
| Release | : 2011 |
| Genre | : Mathematics |
| ISBN | : 0821848496 |
This volume represents the proceedings of the Noncommutative Geometry Workshop that was held as part of the thematic program on operator algebras at the Fields Institute in May 2008. Pioneered by Alain Connes starting in the late 1970s, noncommutative geometry was originally inspired by global analysis, topology, operator algebras, and quantum physics. Its main applications were to settle some long-standing conjectures, such as the Novikov conjecture and the Baum-Connes conjecture. Next came the impact of spectral geometry and the way the spectrum of a geometric operator, like the Laplacian, holds information about the geometry and topology of a manifold, as in the celebrated Weyl law. This has now been vastly generalized through Connes' notion of spectral triples. Finally, recent years have witnessed the impact of number theory, algebraic geometry and the theory of motives, and quantum field theory on noncommutative geometry. Almost all of these aspects are touched upon with new results in the papers of this volume. This book is intended for graduate students and researchers in both mathematics and theoretical physics who are interested in noncommutative geometry and its applications.
Dynamics and Processes
| Author | : P. Blanchard |
| Publisher | : Springer |
| Total Pages | : 220 |
| Release | : 2006-11-14 |
| Genre | : Science |
| ISBN | : 3540386912 |
Lectures on the Mathematics of Quantum Mechanics I
| Author | : Gianfausto Dell'Antonio |
| Publisher | : Springer |
| Total Pages | : 470 |
| Release | : 2015-05-25 |
| Genre | : Science |
| ISBN | : 9462391181 |
The first volume (General Theory) differs from most textbooks as it emphasizes the mathematical structure and mathematical rigor, while being adapted to the teaching the first semester of an advanced course in Quantum Mechanics (the content of the book are the lectures of courses actually delivered.). It differs also from the very few texts in Quantum Mechanics that give emphasis to the mathematical aspects because this book, being written as Lecture Notes, has the structure of lectures delivered in a course, namely introduction of the problem, outline of the relevant points, mathematical tools needed, theorems, proofs. This makes this book particularly useful for self-study and for instructors in the preparation of a second course in Quantum Mechanics (after a first basic course). With some minor additions it can be used also as a basis of a first course in Quantum Mechanics for students in mathematics curricula. The second part (Selected Topics) are lecture notes of a more advanced course aimed at giving the basic notions necessary to do research in several areas of mathematical physics connected with quantum mechanics, from solid state to singular interactions, many body theory, semi-classical analysis, quantum statistical mechanics. The structure of this book is suitable for a second-semester course, in which the lectures are meant to provide, in addition to theorems and proofs, an overview of a more specific subject and hints to the direction of research. In this respect and for the width of subjects this second volume differs from other monographs on Quantum Mechanics. The second volume can be useful for students who want to have a basic preparation for doing research and for instructors who may want to use it as a basis for the presentation of selected topics.
On Quanta, Mind and Matter
| Author | : Harald Atmanspacher |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 394 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 9401145814 |
INSTEAD OF A "FESTSCHRIFT" In June 1998 Hans Primas turned 70 years old. Although he himself is not fond of jubilees and although he likes to play the decimal system of numbers down as contingent, this is nevertheless a suitable occasion to reflect on the professional work of one of the rare distinguished contempo rary scientists who attach equal importance to experimental and theoretical and conceptual lines of research. Hans Primas' interests have covered an enormous range: methods and instruments for nuclear magnetic resonance, theoretical chemistry, C* - and W* -algebraic formulations of quantum me chanics, the measurement problem and its various implications, holism and realism in quantum theory, theory reduction, the work and personality of Wolfgang Pauli, as well as Jungian psychology. In many of these fields he provided important and original food for thought, in some cases going far beyond the everyday business in the scien tific world. As is the case with other scientists who are conceptually inno vative, Hans Primas is read more than he is quoted. His influence is due to his writings. Even with the current flood of publications, he still performs the miracle of having scientists eagerly awaiting his next publication.
Deep Beauty
| Author | : Hans Halvorson |
| Publisher | : Cambridge University Press |
| Total Pages | : 487 |
| Release | : 2011-04-18 |
| Genre | : Mathematics |
| ISBN | : 113949922X |
No scientific theory has caused more puzzlement and confusion than quantum theory. Physics is supposed to help us to understand the world, but quantum theory makes it seem a very strange place. This book is about how mathematical innovation can help us gain deeper insight into the structure of the physical world. Chapters by top researchers in the mathematical foundations of physics explore new ideas, especially novel mathematical concepts at the cutting edge of future physics. These creative developments in mathematics may catalyze the advances that enable us to understand our current physical theories, especially quantum theory. The authors bring diverse perspectives, unified only by the attempt to introduce fresh concepts that will open up new vistas in our understanding of future physics.
Noncommutative Geometry
| Author | : Igor V. Nikolaev |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 400 |
| Release | : 2022-07-18 |
| Genre | : Mathematics |
| ISBN | : 3110788705 |
Noncommutative geometry studies an interplay between spatial forms and algebras with non-commutative multiplication. This book covers the key concepts of noncommutative geometry and its applications in topology, algebraic geometry, and number theory. Our presentation is accessible to the graduate students as well as nonexperts in the field. The second edition includes two new chapters on arithmetic topology and quantum arithmetic.
Encyclopaedia of Mathematics
| Author | : Michiel Hazewinkel |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 543 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 9401512337 |
This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fme subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.
On Klauder's Path: A Field Trip
| Author | : Gerard Gustav Emch |
| Publisher | : World Scientific |
| Total Pages | : 286 |
| Release | : 1994-04-27 |
| Genre | : Science |
| ISBN | : 9814502278 |
This volume contains contributions by friends, colleagues and associates of John R Klauder on the occasion of his 60th birthday.Klauder's scientific work embraces vast territories from quantum theories to general relativity, optics and chaotic dynamics. A recurrent theme in his research is the role played by coherent states, in particular, in connection with path integral formulations of quantization. Perhaps at a less lofty level, this concept has had at least two spectacular applications: as a powerful investigative tool in quantum optics and as a precursor to wavelets. In a different vein, Klauder also attacked specific, non-renormalizable but exactly soluble, hard-core models in field theory, where he uncovered what has since been called the Klauder phenomenon.The contributors to this volume represent the special brand of mathematicians and physicists John Klauder helped define throughout his seminal career in the industrial and academic worlds.
