Lectures On Quantum Theory Mathematical And Structural Foundations
Author: Chris J. Isham
Publisher: Allied Publishers
Published: 2001
Total Pages: 278
ISBN-13: 9788177641905
DOWNLOAD EBOOK →Lanterna Rally
eBook PDF Download Digital Library
Lectures on Quantum Theory
Author: C. J. Isham
Publisher: World Scientific Publishing Company Incorporated
Published: 1995-01-01
Total Pages: 220
ISBN-13: 9781860940002
DOWNLOAD EBOOK →This book is based on material taught to final-year physics undergraduates as part of the theoretical physics option at Imperial College. After a self-contained introduction to the essential ideas of vector spaces and linear operators, a bridge is built between the concepts and mathematics of classical physics, and the new mathematical framework employed in quantum mechanics. The axioms of nonrelativistic quantum theory are introduced, and shown to lead to a variety of new conceptual problems. Subjects discussed include state-vector reduction, the problem of measurement, quantum entanglement, the Kochen-Specker theorem, and the Bell inequalities. The book includes twenty-five problems with worked solutions.
Lectures on Groups and Vector Spaces for Physicists
Author: C. J. Isham
Publisher: World Scientific
Published: 1989
Total Pages: 232
ISBN-13: 9789971509552
DOWNLOAD EBOOK →These notes are the contents of a lecture course given to third year physics undergraduates at the Imperial College who are taking the theoretical physics option. The subject of ?Algebra and Groups? is of considerable importance in a number of branches of modern theoretical physics, and therefore one major objective of the course is to introduce the students to the basic ideas on the subject, bearing in mind the potential applications to quantum theory. However, another equally important aim of the course is to introduce the student to the art of genuine ?mathematical? thinking. The notes are therefore written in a more precise mathematical style than is usually the case in courses aimed at physics students. Quite apart from the general educational value of such an exposure to abstract thinking, it is also the case that much modern theoretical physics draws on sophisticated ideas from pure mathematics and therefore it is most important that a perspective graduate student can approach these subjects without experiencing a total culture shock! The course is divided into three parts. The first is a short introduction to general group theory, with particular emphasis being placed on the matrix Lie groups that play such a crucial role in modern theoretical physics. The second part deals with the theory of vector spaces, with particular attention being paid to the theory of Hilbert spaces and the basic analytical techniques that are needed to handle the infinite dimensional situation. The final part of the course is a short introduction to the theory of group representations and the associated theory of characters.
The Structural Foundations of Quantum Gravity
Author: Dean Rickles
Publisher: Clarendon Press
Published: 2006-11-16
Total Pages: 288
ISBN-13: 0191515027
DOWNLOAD EBOOK →Quantum gravity is the name given to a theory that unites general relativity - Einstein's theory of gravitation and spacetime - with quantum field theory, our framework for describing non-gravitational forces. The Structural Foundations of Quantum Gravity brings together philosophers and physicists to discuss a range of conceptual issues that surface in the effort to unite these theories, focusing in particular on the ontological nature of the spacetime that results. Although there has been a great deal written about quantum gravity from the perspective of physicists and mathematicians, very little attention has been paid to the philosophical aspects. This volume closes that gap, with essays written by some of the leading researchers in the field. Individual papers defend or attack a structuralist perspective on the fundamental ontologies of our physical theories, which offers the possibility of shedding new light on a number of foundational problems. It is a book that will be of interest not only to physicists and philosophers of physics but to anyone concerned with foundational issues and curious to explore new directions in our understanding of spacetime and quantum physics.
Quantum Foundations And Open Quantum Systems: Lecture Notes Of The Advanced School
Author: Nieuwenhuizen Theo M
Publisher: World Scientific
Published: 2014-10-03
Total Pages: 612
ISBN-13: 9814616745
DOWNLOAD EBOOK →The Advanced School on Quantum Foundations and Open Quantum Systems was an exceptional combination of lectures. These comprise lectures in standard physics and investigations on the foundations of quantum physics.On the one hand it included lectures on quantum information, quantum open systems, quantum transport and quantum solid state. On the other hand it included lectures on quantum measurement, models for elementary particles, sub-quantum structures and aspects on the philosophy and principles of quantum physics.The special program of this school offered a broad outlook on the current and near future fundamental research in theoretical physics.The lectures are at the level of PhD students.
Progress and Visions in Quantum Theory in View of Gravity
Author: Felix Finster
Publisher: Birkhäuser
Published: 2021-04-10
Total Pages: 295
ISBN-13: 9783030389437
DOWNLOAD EBOOK →This book focuses on a critical discussion of the status and prospects of current approaches in quantum mechanics and quantum field theory, in particular concerning gravity. It contains a carefully selected cross-section of lectures and discussions at the seventh conference “Progress and Visions in Quantum Theory in View of Gravity” which took place in fall 2018 at the Max Planck Institute for Mathematics in the Sciences in Leipzig. In contrast to usual proceeding volumes, instead of reporting on the most recent technical results, contributors were asked to discuss visions and new ideas in foundational physics, in particular concerning foundations of quantum field theory. A special focus has been put on the question of which physical principles of quantum (field) theory can be considered fundamental in view of gravity. The book is mainly addressed to mathematicians and physicists who are interested in fundamental questions of mathematical physics. It allows the reader to obtain a broad and up-to-date overview of a fascinating active research area.
Fundamental Mathematical Structures of Quantum Theory
Author: Valter Moretti
Publisher: Springer
Published: 2019-06-20
Total Pages: 345
ISBN-13: 3030183467
DOWNLOAD EBOOK →This textbook presents in a concise and self-contained way the advanced fundamental mathematical structures in quantum theory. It is based on lectures prepared for a 6 months course for MSc students. The reader is introduced to the beautiful interconnection between logic, lattice theory, general probability theory, and general spectral theory including the basic theory of von Neumann algebras and of the algebraic formulation, naturally arising in the study of the mathematical machinery of quantum theories. Some general results concerning hidden-variable interpretations of QM such as Gleason's and the Kochen-Specker theorems and the related notions of realism and non-contextuality are carefully discussed. This is done also in relation with the famous Bell (BCHSH) inequality concerning local causality. Written in a didactic style, this book includes many examples and solved exercises. The work is organized as follows. Chapter 1 reviews some elementary facts and properties of quantum systems. Chapter 2 and 3 present the main results of spectral analysis in complex Hilbert spaces. Chapter 4 introduces the point of view of the orthomodular lattices' theory. Quantum theory form this perspective turns out to the probability measure theory on the non-Boolean lattice of elementary observables and Gleason's theorem characterizes all these measures. Chapter 5 deals with some philosophical and interpretative aspects of quantum theory like hidden-variable formulations of QM. The Kochen-Specker theorem and its implications are analyzed also in relation BCHSH inequality, entanglement, realism, locality, and non-contextuality. Chapter 6 focuses on the algebra of observables also in the presence of superselection rules introducing the notion of von Neumann algebra. Chapter 7 offers the idea of (groups of) quantum symmetry, in particular, illustrated in terms of Wigner and Kadison theorems. Chapter 8 deals with the elementary ideas and results of the so called algebraic formulation of quantum theories in terms of both *-algebras and C*-algebras. This book should appeal to a dual readership: on one hand mathematicians that wish to acquire the tools that unlock the physical aspects of quantum theories; on the other physicists eager to solidify their understanding of the mathematical scaffolding of quantum theories.
Lectures on Quantum Mechanics
Author: Paul A. M. Dirac
Publisher: Courier Corporation
Published: 2013-05-27
Total Pages: 96
ISBN-13: 0486320286
DOWNLOAD EBOOK →Four concise, brilliant lectures on mathematical methods in quantum mechanics from Nobel Prize–winning quantum pioneer build on idea of visualizing quantum theory through the use of classical mechanics.
Integrable Systems, Quantum Groups, and Quantum Field Theories
Author: Alberto Ibort
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 508
ISBN-13: 9401119805
DOWNLOAD EBOOK →In many ways the last decade has witnessed a surge of interest in the interplay between theoretical physics and some traditional areas of pure mathematics. This book contains the lectures delivered at the NATO-ASI Summer School on `Recent Problems in Mathematical Physics' held at Salamanca, Spain (1992), offering a pedagogical and updated approach to some of the problems that have been at the heart of these events. Among them, we should mention the new mathematical structures related to integrability and quantum field theories, such as quantum groups, conformal field theories, integrable statistical models, and topological quantum field theories, that are discussed at length by some of the leading experts on the areas in several of the lectures contained in the book. Apart from these, traditional and new problems in quantum gravity are reviewed. Other contributions to the School included in the book range from symmetries in partial differential equations to geometrical phases in quantum physics. The book is addressed to researchers in the fields covered, PhD students and any scientist interested in obtaining an updated view of the subjects.
Foundations of Quantum Theory
Author: E.M. Rasel
Publisher: IOS Press
Published: 2019-01-23
Total Pages: 432
ISBN-13: 1614999376
DOWNLOAD EBOOK →This volume provides a summary of the lectures presented at the International School of Physics "Enrico Fermi" on the Foundations of Quantum Theory, organized by the Italian Physical Society in Varenna, Italy from 8-13 July 2016, in collaboration with the Wilhelm und Else Heraeus-Stiftung. It was the first "Enrico Fermi" Summer School on this topic since 1977. Its main goal was to provide an overview of the recent theoretical and experimental developments in an active field of research, the foundations of quantum mechanics. The field is characterized by a dichotomy of unparalleled agreement between theory and experiment on the one hand, and an enormous variety of interpretations of the underlying mathematical formalism on the other hand. This proceedings of the "Enrico Fermi" Summer School of July 2016 contains 21 contributions on a range of topics: the history and interpretations of quantum theory; the principle of complementarity and wave-particle duality; quantum theory from first principles; the reality of the wave function; the concept of the photon; measurement in quantum theory; the interface of quantum theory and general relativity; and quantum optical tests of quantum theory.
