Spinors in Hilbert Space

Spinors in Hilbert Space

Author: Paul Dirac

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 97

ISBN-13: 1475700342

DOWNLOAD EBOOK

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.


Book Synopsis Spinors in Hilbert Space by : Paul Dirac

Download or read book Spinors in Hilbert Space written by Paul Dirac and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 97 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Spinors in Hilbert Space

Spinors in Hilbert Space

Author: Paul Adrien Maurice Dirac

Publisher:

Published: 1970

Total Pages: 200

ISBN-13:

DOWNLOAD EBOOK


Book Synopsis Spinors in Hilbert Space by : Paul Adrien Maurice Dirac

Download or read book Spinors in Hilbert Space written by Paul Adrien Maurice Dirac and published by . This book was released on 1970 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Spinors in Hilbert Space

Spinors in Hilbert Space

Author: Roger Plymen

Publisher: Cambridge University Press

Published: 1994-12

Total Pages: 192

ISBN-13: 9780521450225

DOWNLOAD EBOOK

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


Book Synopsis Spinors in Hilbert Space by : Roger Plymen

Download or read book Spinors in Hilbert Space written by Roger Plymen and published by Cambridge University Press. This book was released on 1994-12 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: A definitive self-contained account of the subject. Of appeal to a wide audience in mathematics and physics.

Theory Of Spinors: An Introduction

Theory Of Spinors: An Introduction

Author: Moshe Carmeli

Publisher: World Scientific Publishing Company

Published: 2000-04-12

Total Pages: 228

ISBN-13: 9813102764

DOWNLOAD EBOOK

Spinors are used extensively in physics. It is widely accepted that they are more fundamental than tensors, and the easy way to see this is through the results obtained in general relativity theory by using spinors — results that could not have been obtained by using tensor methods only.The foundation of the concept of spinors is groups; spinors appear as representations of groups. This textbook expounds the relationship between spinors and representations of groups. As is well known, spinors and representations are both widely used in the theory of elementary particles.The authors present the origin of spinors from representation theory, but nevertheless apply the theory of spinors to general relativity theory, and part of the book is devoted to curved space-time applications.Based on lectures given at Ben Gurion University, this textbook is intended for advanced undergraduate and graduate students in physics and mathematics, as well as being a reference for researchers.


Book Synopsis Theory Of Spinors: An Introduction by : Moshe Carmeli

Download or read book Theory Of Spinors: An Introduction written by Moshe Carmeli and published by World Scientific Publishing Company. This book was released on 2000-04-12 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spinors are used extensively in physics. It is widely accepted that they are more fundamental than tensors, and the easy way to see this is through the results obtained in general relativity theory by using spinors — results that could not have been obtained by using tensor methods only.The foundation of the concept of spinors is groups; spinors appear as representations of groups. This textbook expounds the relationship between spinors and representations of groups. As is well known, spinors and representations are both widely used in the theory of elementary particles.The authors present the origin of spinors from representation theory, but nevertheless apply the theory of spinors to general relativity theory, and part of the book is devoted to curved space-time applications.Based on lectures given at Ben Gurion University, this textbook is intended for advanced undergraduate and graduate students in physics and mathematics, as well as being a reference for researchers.

Spinors in Four-Dimensional Spaces

Spinors in Four-Dimensional Spaces

Author: Gerardo F. Torres del Castillo

Publisher: Springer Science & Business Media

Published: 2010-07-23

Total Pages: 182

ISBN-13: 0817649840

DOWNLOAD EBOOK

Without using the customary Clifford algebras frequently studied in connection with the representations of orthogonal groups, this book gives an elementary introduction to the two-component spinor formalism for four-dimensional spaces with any signature. Some of the useful applications of four-dimensional spinors, such as Yang–Mills theory, are derived in detail using illustrative examples. Spinors in Four-Dimensional Spaces is aimed at graduate students and researchers in mathematical and theoretical physics interested in the applications of the two-component spinor formalism in any four-dimensional vector space or Riemannian manifold with a definite or indefinite metric tensor. This systematic and self-contained book is suitable as a seminar text, a reference book, and a self-study guide.


Book Synopsis Spinors in Four-Dimensional Spaces by : Gerardo F. Torres del Castillo

Download or read book Spinors in Four-Dimensional Spaces written by Gerardo F. Torres del Castillo and published by Springer Science & Business Media. This book was released on 2010-07-23 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: Without using the customary Clifford algebras frequently studied in connection with the representations of orthogonal groups, this book gives an elementary introduction to the two-component spinor formalism for four-dimensional spaces with any signature. Some of the useful applications of four-dimensional spinors, such as Yang–Mills theory, are derived in detail using illustrative examples. Spinors in Four-Dimensional Spaces is aimed at graduate students and researchers in mathematical and theoretical physics interested in the applications of the two-component spinor formalism in any four-dimensional vector space or Riemannian manifold with a definite or indefinite metric tensor. This systematic and self-contained book is suitable as a seminar text, a reference book, and a self-study guide.

A Primer on Hilbert Space Theory

A Primer on Hilbert Space Theory

Author: Carlo Alabiso

Publisher: Springer Nature

Published: 2021-03-03

Total Pages: 343

ISBN-13: 3030674177

DOWNLOAD EBOOK

This book offers an essential introduction to the theory of Hilbert space, a fundamental tool for non-relativistic quantum mechanics. Linear, topological, metric, and normed spaces are all addressed in detail, in a rigorous but reader-friendly fashion. The rationale for providing an introduction to the theory of Hilbert space, rather than a detailed study of Hilbert space theory itself, lies in the strenuous mathematics demands that even the simplest physical cases entail. Graduate courses in physics rarely offer enough time to cover the theory of Hilbert space and operators, as well as distribution theory, with sufficient mathematical rigor. Accordingly, compromises must be found between full rigor and the practical use of the instruments. Based on one of the authors’s lectures on functional analysis for graduate students in physics, the book will equip readers to approach Hilbert space and, subsequently, rigged Hilbert space, with a more practical attitude. It also includes a brief introduction to topological groups, and to other mathematical structures akin to Hilbert space. Exercises and solved problems accompany the main text, offering readers opportunities to deepen their understanding. The topics and their presentation have been chosen with the goal of quickly, yet rigorously and effectively, preparing readers for the intricacies of Hilbert space. Consequently, some topics, e.g., the Lebesgue integral, are treated in a somewhat unorthodox manner. The book is ideally suited for use in upper undergraduate and lower graduate courses, both in Physics and in Mathematics.


Book Synopsis A Primer on Hilbert Space Theory by : Carlo Alabiso

Download or read book A Primer on Hilbert Space Theory written by Carlo Alabiso and published by Springer Nature. This book was released on 2021-03-03 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an essential introduction to the theory of Hilbert space, a fundamental tool for non-relativistic quantum mechanics. Linear, topological, metric, and normed spaces are all addressed in detail, in a rigorous but reader-friendly fashion. The rationale for providing an introduction to the theory of Hilbert space, rather than a detailed study of Hilbert space theory itself, lies in the strenuous mathematics demands that even the simplest physical cases entail. Graduate courses in physics rarely offer enough time to cover the theory of Hilbert space and operators, as well as distribution theory, with sufficient mathematical rigor. Accordingly, compromises must be found between full rigor and the practical use of the instruments. Based on one of the authors’s lectures on functional analysis for graduate students in physics, the book will equip readers to approach Hilbert space and, subsequently, rigged Hilbert space, with a more practical attitude. It also includes a brief introduction to topological groups, and to other mathematical structures akin to Hilbert space. Exercises and solved problems accompany the main text, offering readers opportunities to deepen their understanding. The topics and their presentation have been chosen with the goal of quickly, yet rigorously and effectively, preparing readers for the intricacies of Hilbert space. Consequently, some topics, e.g., the Lebesgue integral, are treated in a somewhat unorthodox manner. The book is ideally suited for use in upper undergraduate and lower graduate courses, both in Physics and in Mathematics.

An Introduction to Hilbert Space and Quantum Logic

An Introduction to Hilbert Space and Quantum Logic

Author: David W. Cohen

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 159

ISBN-13: 1461388414

DOWNLOAD EBOOK

Historically, nonclassical physics developed in three stages. First came a collection of ad hoc assumptions and then a cookbook of equations known as "quantum mechanics". The equations and their philosophical underpinnings were then collected into a model based on the mathematics of Hilbert space. From the Hilbert space model came the abstaction of "quantum logics". This book explores all three stages, but not in historical order. Instead, in an effort to illustrate how physics and abstract mathematics influence each other we hop back and forth between a purely mathematical development of Hilbert space, and a physically motivated definition of a logic, partially linking the two throughout, and then bringing them together at the deepest level in the last two chapters. This book should be accessible to undergraduate and beginning graduate students in both mathematics and physics. The only strict prerequisites are calculus and linear algebra, but the level of mathematical sophistication assumes at least one or two intermediate courses, for example in mathematical analysis or advanced calculus. No background in physics is assumed.


Book Synopsis An Introduction to Hilbert Space and Quantum Logic by : David W. Cohen

Download or read book An Introduction to Hilbert Space and Quantum Logic written by David W. Cohen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: Historically, nonclassical physics developed in three stages. First came a collection of ad hoc assumptions and then a cookbook of equations known as "quantum mechanics". The equations and their philosophical underpinnings were then collected into a model based on the mathematics of Hilbert space. From the Hilbert space model came the abstaction of "quantum logics". This book explores all three stages, but not in historical order. Instead, in an effort to illustrate how physics and abstract mathematics influence each other we hop back and forth between a purely mathematical development of Hilbert space, and a physically motivated definition of a logic, partially linking the two throughout, and then bringing them together at the deepest level in the last two chapters. This book should be accessible to undergraduate and beginning graduate students in both mathematics and physics. The only strict prerequisites are calculus and linear algebra, but the level of mathematical sophistication assumes at least one or two intermediate courses, for example in mathematical analysis or advanced calculus. No background in physics is assumed.

Spinors In Physics And Geometry

Spinors In Physics And Geometry

Author: Giuseppe Furlan

Publisher: World Scientific

Published: 1988-11-01

Total Pages: 368

ISBN-13: 9814644447

DOWNLOAD EBOOK

This conference brought together physicists and mathematicians working on spinors, which have played an important role in recent research on supersymmetry, Kaluza-Klein theories, twistors and general relativity.


Book Synopsis Spinors In Physics And Geometry by : Giuseppe Furlan

Download or read book Spinors In Physics And Geometry written by Giuseppe Furlan and published by World Scientific. This book was released on 1988-11-01 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: This conference brought together physicists and mathematicians working on spinors, which have played an important role in recent research on supersymmetry, Kaluza-Klein theories, twistors and general relativity.

Twenty-First Century Quantum Mechanics: Hilbert Space to Quantum Computers

Twenty-First Century Quantum Mechanics: Hilbert Space to Quantum Computers

Author: Guido Fano

Publisher: Springer

Published: 2017-06-27

Total Pages: 271

ISBN-13: 3319587323

DOWNLOAD EBOOK

This book is designed to make accessible to nonspecialists the still evolving concepts of quantum mechanics and the terminology in which these are expressed. The opening chapters summarize elementary concepts of twentieth century quantum mechanics and describe the mathematical methods employed in the field, with clear explanation of, for example, Hilbert space, complex variables, complex vector spaces and Dirac notation, and the Heisenberg uncertainty principle. After detailed discussion of the Schrödinger equation, subsequent chapters focus on isotropic vectors, used to construct spinors, and on conceptual problems associated with measurement, superposition, and decoherence in quantum systems. Here, due attention is paid to Bell’s inequality and the possible existence of hidden variables. Finally, progression toward quantum computation is examined in detail: if quantum computers can be made practicable, enormous enhancements in computing power, artificial intelligence, and secure communication will result. This book will be of interest to a wide readership seeking to understand modern quantum mechanics and its potential applications.


Book Synopsis Twenty-First Century Quantum Mechanics: Hilbert Space to Quantum Computers by : Guido Fano

Download or read book Twenty-First Century Quantum Mechanics: Hilbert Space to Quantum Computers written by Guido Fano and published by Springer. This book was released on 2017-06-27 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is designed to make accessible to nonspecialists the still evolving concepts of quantum mechanics and the terminology in which these are expressed. The opening chapters summarize elementary concepts of twentieth century quantum mechanics and describe the mathematical methods employed in the field, with clear explanation of, for example, Hilbert space, complex variables, complex vector spaces and Dirac notation, and the Heisenberg uncertainty principle. After detailed discussion of the Schrödinger equation, subsequent chapters focus on isotropic vectors, used to construct spinors, and on conceptual problems associated with measurement, superposition, and decoherence in quantum systems. Here, due attention is paid to Bell’s inequality and the possible existence of hidden variables. Finally, progression toward quantum computation is examined in detail: if quantum computers can be made practicable, enormous enhancements in computing power, artificial intelligence, and secure communication will result. This book will be of interest to a wide readership seeking to understand modern quantum mechanics and its potential applications.

Hilbert Space Operators in Quantum Physics

Hilbert Space Operators in Quantum Physics

Author: Jirí Blank

Publisher: Springer Science & Business Media

Published: 1999-04-23

Total Pages: 626

ISBN-13: 9781563961427

DOWNLOAD EBOOK

Market: Mathematicians, researchers, teachers, and graduate students specializing in quantum physics, mathematical physics, and applied mathematics. "I really enjoyed reading this work. It is very well written, by three real experts in the field. It stands quite alone....The translation is remarkably good." John R. Taylor, University of Colorado Based on lectures delivered over the past two decades, this book explains in detail the theory of linear Hilbert-space operators and its uses in quantum physics. The central mathematical tool of this book is the spectral theory of self-adjoint operators, which together with functional analysis and an introduction to the theory of operator sets and algebras, is used in a systematic analysis of the operator aspect of quantum theory. In addition, the theory of Hilbert-space operators is discussed in conjunction with various applications such as Schrodinger operators and scattering theory.


Book Synopsis Hilbert Space Operators in Quantum Physics by : Jirí Blank

Download or read book Hilbert Space Operators in Quantum Physics written by Jirí Blank and published by Springer Science & Business Media. This book was released on 1999-04-23 with total page 626 pages. Available in PDF, EPUB and Kindle. Book excerpt: Market: Mathematicians, researchers, teachers, and graduate students specializing in quantum physics, mathematical physics, and applied mathematics. "I really enjoyed reading this work. It is very well written, by three real experts in the field. It stands quite alone....The translation is remarkably good." John R. Taylor, University of Colorado Based on lectures delivered over the past two decades, this book explains in detail the theory of linear Hilbert-space operators and its uses in quantum physics. The central mathematical tool of this book is the spectral theory of self-adjoint operators, which together with functional analysis and an introduction to the theory of operator sets and algebras, is used in a systematic analysis of the operator aspect of quantum theory. In addition, the theory of Hilbert-space operators is discussed in conjunction with various applications such as Schrodinger operators and scattering theory.