Spinors in Hilbert Space

Author: Roger Plymen,Paul Robinson

Publisher: Cambridge University Press

ISBN: 9780521450225

Category: Mathematics

Page: 165

View: 4818

A definitive self-contained account of the subject. Of appeal to a wide audience in mathematics and physics.
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Global Differential Geometry

Author: Christian Bär,Joachim Lohkamp,Matthias Schwarz

Publisher: Springer Science & Business Media

ISBN: 3642228429

Category: Mathematics

Page: 524

View: 6070

This volume contains a collection of well-written surveys provided by experts in Global Differential Geometry to give an overview over recent developments in Riemannian Geometry, Geometric Analysis and Symplectic Geometry. The papers are written for graduate students and researchers with a general interest in geometry, who want to get acquainted with the current trends in these central fields of modern mathematics.
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Quantum Probability Communications Qp-Pq

Author: J. M Lindsay

Publisher: World Scientific

ISBN: 9812389598

Category: Science

Page: 284

View: 3299

Lecture notes from a Summer School on Quantum Probability held at the University of Grenoble are collected in these two volumes of the QP-PQ series. The articles have been refereed and extensively revised for publication. It is hoped that both current and future students of quantum probability will be engaged, informed and inspired by the contents of these two volumes. An extensive bibliography containing the references from all the lectures is included in Volume 12.
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Restricted Orbit Equivalence for Actions of Discrete Amenable Groups

Author: Janet Whalen Kammeyer,Daniel J. Rudolph

Publisher: Cambridge University Press

ISBN: 9780521807951

Category: Mathematics

Page: 201

View: 1351

This monograph offers a broad investigative tool in ergodic theory and measurable dynamics. The motivation for this work is that one may measure how similar two dynamical systems are by asking how much the time structure of orbits of one system must be distorted for it to become the other. Different restrictions on the allowed distortion will lead to different restricted orbit equivalence theories. These include Ornstein's Isomorphism theory, Kakutani Equivalence theory and a list of others. By putting such restrictions in an axiomatic framework, a general approach is developed that encompasses all of these examples simultaneously and gives insight into how to seek further applications.
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Cox Rings

Author: Ivan Arzhantsev,Ulrich Derenthal,Jürgen Hausen,Antonio Laface

Publisher: Cambridge University Press

ISBN: 1107024625

Category: Mathematics

Page: 472

View: 2546

This book provides a largely self-contained introduction to Cox rings and their applications in algebraic and arithmetic geometry.
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Mathematics of Quantization and Quantum Fields

Author: Jan Dereziński,Christian Gérard

Publisher: Cambridge University Press

ISBN: 1107011116

Category: Science

Page: 674

View: 3504

A unique and definitive review of mathematical aspects of quantization and quantum field theory for graduate students and researchers.
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Books in Print

Author: N.A

Publisher: N.A

ISBN: N.A

Category: American literature

Page: N.A

View: 9127

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Spinors in Hilbert Space

Author: Paul Dirac

Publisher: Springer Science & Business Media

ISBN: 1475700342

Category: Science

Page: 91

View: 3736

1. Hilbert Space The words "Hilbert space" here will always denote what math ematicians call a separable Hilbert space. It is composed of vectors each with a denumerable infinity of coordinates ql' q2' Q3, .... Usually the coordinates are considered to be complex numbers and each vector has a squared length ~rIQrI2. This squared length must converge in order that the q's may specify a Hilbert vector. Let us express qr in terms of real and imaginary parts, qr = Xr + iYr' Then the squared length is l:.r(x; + y;). The x's and y's may be looked upon as the coordinates of a vector. It is again a Hilbert vector, but it is a real Hilbert vector, with only real coordinates. Thus a complex Hilbert vector uniquely determines a real Hilbert vector. The second vector has, at first sight, twice as many coordinates as the first one. But twice a denumerable in finity is again a denumerable infinity, so the second vector has the same number of coordinates as the first. Thus a complex Hilbert vector is not a more general kind of quantity than a real one.
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Basic Noncommutative Geometry

Author: Masoud Khalkhali

Publisher: European Mathematical Society

ISBN: 9783037190616

Category: Mathematics

Page: 223

View: 5761

"Basic Noncommutative Geometry provides an introduction to noncommutative geometry and some of its applications. The book can be used either as a textbook for a graduate course on the subject or for self-study. It will be useful for graduate students and researchers in mathematics and theoretical physics and all those who are interested in gaining an understanding of the subject. One feature of this book is the wealth of examples and exercises that help the reader to navigate through the subject. While background material is provided in the text and in several appendices, some familiarity with basic notions of functional analysis, algebraic topology, differential geometry and homological algebra at a first year graduate level is helpful. Developed by Alain Connes since the late 1970s, noncommutative geometry has found many applications to long-standing conjectures in topology and geometry and has recently made headways in theoretical physics and number theory. The book starts with a detailed description of some of the most pertinent algebra-geometry correspondences by casting geometric notions in algebraic terms, then proceeds in the second chapter to the idea of a noncommutative space and how it is constructed. The last two chapters deal with homological tools: cyclic cohomology and Connes-Chern characters in K-theory and K-homology, culminating in one commutative diagram expressing the equality of topological and analytic index in a noncommutative setting. Applications to integrality of noncommutative topological invariants are given as well."--Publisher's description.
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Tensors

Geometry and Applications

Author: J. M. Landsberg

Publisher: American Mathematical Soc.

ISBN: 0821869078

Category: Mathematics

Page: 439

View: 3782

Tensors are ubiquitous in the sciences. The geometry of tensors is both a powerful tool for extracting information from data sets, and a beautiful subject in its own right. This book has three intended uses: a classroom textbook, a reference work for researchers in the sciences, and an account of classical and modern results in (aspects of) the theory that will be of interest to researchers in geometry. For classroom use, there is a modern introduction to multilinear algebra and to the geometry and representation theory needed to study tensors, including a large number of exercises. For researchers in the sciences, there is information on tensors in table format for easy reference and a summary of the state of the art in elementary language. This is the first book containing many classical results regarding tensors. Particular applications treated in the book include the complexity of matrix multiplication, P versus NP, signal processing, phylogenetics, and algebraic statistics. For geometers, there is material on secant varieties, G-varieties, spaces with finitely many orbits and how these objects arise in applications, discussions of numerous open questions in geometry arising in applications, and expositions of advanced topics such as the proof of the Alexander-Hirschowitz theorem and of the Weyman-Kempf method for computing syzygies.
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