Table of Contents Preface 1 Foundations 1 2 Why Geometry, so Physics, Require Complex Numbers 25 3 Properties of Statefunctions 38 4 The Foundations of Coherent Superposition 58 5 Geometry, Transformations, Groups and Observers 85 6 The Poincare Group and Its Implications 108 7 The Dimension of Space 122 8 Bosons, Fermions, Spinors and Orthogonal Groups 146 9 The Complete Reasonableness of Quantum Mechanics 159 A: Terminology and Conventions 177 The Einstein Podolsky Rosen Paradox 185 Experimental Meaning of the Concept of Identical Particles 191 Nonexistence of Superselection Rules; Definition of Term "Frame of Reference" 203 Complex Groups, Quantum Mechanics, and the Dimension and Reality of Space 221 The Reality and Dimension of Space and the Complexity of Quantum Mechanics 235 References 255 Index 259.

A graduate level text which systematically lays out the foundations of Quantum Groups.

Quantum Theory, together with the principles of special and general relativity, constitute a scientific revolution that has profoundly influenced the way in which we think about the universe and the fundamental forces that govern it. The Historical Development of Quantum Theory is a definitive historical study of that scientific work and the human struggles that accompanied it from the beginning. Drawing upon such materials as the resources of the Archives for the History of Quantum Physics, the Niels Bohr Archives, and the archives and scientific correspondence of the principal quantum physicists, as well as Jagdish Mehra's personal discussions over many years with most of the architects of quantum theory, the authors have written a rigorous scientific history of quantum theory in a deeply human context. This multivolume work presents a rich account of an intellectual triumph: a unique analysis of the creative scientific process. The Historical Development of Quantum Theory is science, history, and biography, all wrapped in the story of a great human enterprise. Its lessons will be an aid to those working in the sciences and humanities alike.

This book discusses a link between statistical theory and quantum theory based on the concept of epistemic processes. The latter are processes, such as statistical investigations or quantum mechanical measurements, that can be used to obtain knowledge about something. Various topics in quantum theory are addressed, including the construction of a Hilbert space from reasonable assumptions and an interpretation of quantum states. Separate derivations of the Born formula and the one-dimensional Schrödinger equation are given. In concrete terms, a Hilbert space can be constructed under some technical assumptions associated with situations where there are two conceptual variables that can be seen as maximally accessible. Then to every accessible conceptual variable there corresponds an operator on this Hilbert space, and if the variables take a finite number of values, the eigenspaces/eigenvectors of these operators correspond to specific questions in nature together with sharp answers to these questions. This paves a new way to the foundations of quantum theory. The resulting interpretation of quantum mechanics is related to Hervé Zwirn's recent Convivial Solipsism, but it also has some relations to Quantum Bayesianism and to Rovelli's relational quantum mechanics. Niels Bohr's concept of complementarity plays an important role. Philosophical implications of this approach to quantum theory are discussed, including consequences for macroscopic settings. The book will benefit a broad readership, including physicists and statisticians interested in the foundations of their disciplines, philosophers of science and graduate students, and anyone with a reasonably good background in mathematics and an open mind.

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Preface 1 The Physical Meaning of Poincare Massless Representations 1 2 Massless Representations 12 3 Massless Fields are Different 32 4 How to Couple Massless and Massive Matter 56 5 The Behavior of Matter in Fields 73 6 Geometrical Reasons for the Poincare Group 95 7 Description of the Electromagnetic Field 123 8 The Equations Governing Free Gravitation 135 9 How Matter Determines Gravitational Fields 150 10 Nonlinearity and Geometry 165 11 Quantum Gravity 183 References 201 Index 207.

Based on eight extensive lectures selected from those given at the renowned Chris Engelbrecht Summer School in Theoretical Physics in South Africa, this text on the theoretical foundations of quantum information processing and communication covers an array of topics, including quantum probabilities, open systems, and non-Markovian dynamics and decoherence. It also addresses quantum information and relativity as well as testing quantum mechanics in high energy physics. Because these self-contained lectures discuss topics not typically covered in advanced undergraduate courses, they are ideal for post-graduate students entering this field of research. Some of the lectures are written at a more introductory level while others are presented as tutorials that survey recent developments and results in various subfields.

This book is by far the most comprehensive treatment of point and space groups, and their meaning and applications. Its completeness makes it especially useful as a text, since it gives the instructor the flexibility to best fit the class and goals. The instructor, not the author, decides what is in the course. And it is the prime book for reference, as material is much more likely to be found in it than in any other book; it also provides detailed guides to other sources. Much of what is taught is folklore, things everyone knows are true, but (almost?) no one knows why, or has seen proofs, justifications, rationales or explanations. (Why are there 14 Bravais lattices, and why these? Are the reasons geometrical, conventional or both? What determines the Wigner–Seitz cells? How do they affect the number of Bravais lattices? Why are symmetry groups relevant to molecules whose vibrations make them unsymmetrical? And so on). Here these analyses are given, interrelated, and in-depth. The understanding so obtained gives a strong foundation for application and extension. Assumptions and restrictions are not merely made explicit, but also emphasized. In order to provide so much information, details and examples, and ways of helping readers learn and understand, the book contains many topics found nowhere else, or only in obscure articles from the distant past. The treatment is (often completely) different from those elsewhere. At least in the explanations, and usually in many other ways, the book is completely new and fresh. It is designed to inform, educate and make the reader think. It strongly emphasizes understanding. The book can be used at many levels, by many different classes of readers — from those who merely want brief explanations (perhaps just of terminology), who just want to skim, to those who wish the most thorough understanding. Request Inspection Copy

WHY GOD COULD NOT CREATE THE UNIVERSE WITH A DIFFERENT DIMENSION EVEN IF IT WANTED TO or perhaps anything else. Perhaps the universe must be the way it is. It seems that what is omnipotent is mathematics, elementary arithmetic, just counting. Yet even mathematics is not powerful enough to create a universe¿there are just too many conditions, conflicting. Existence is impossible. Beyond that for there to be structure is quite inconceivable. But the universe does exist, there are galaxies, stars, even the possibility of life. That life is possible merely allows it to exist but only with the greatest good fortune does it actually occur. Intelligence is vastly less likely, ability and technology far more improbable. That we are, what we are, seem so strange, inconceivable, that we are left merely with wonder¿and, as we seem unable to realize, the need for the deepest care, responsibility and gratitude. We have been given by the unbelievable benevolence of chance, no life, but life with the most wondrous part of the universe, the ability to think, to know, to create, to wonder¿and thus the demand that we use our most awesome gifts to protect them, to protect and preserve the world in which they exist, and the life, likely so rare if not unique in the universe, which has received these astounding favors of chance, that has been given by nature its most exalted constituents. What we are requires that we enhance what we are, what we are part of, to see, understand and be grateful. An exploration of the precise conditions required for the existence of humans in the universe. ...the author does an admirable job delineating the laws of physics without becoming too bogged down in complicated jargon, and he maintains a sense of wonder about the unique and random nature of the universe. He repeatedly celebrates our highly improbable achievements as a species, marveling at our ability to use the language of abstract mathematics to unravel the mysteries of existence. ... the prevailing tone of the narrative is clear and confident, marked by a meticulous attention to detail. An...often fascinating journey through the history of the universe and mankind. -Kirkus Discoveries

This book studies the foundations of quantum theory through its relationship to classical physics. This idea goes back to the Copenhagen Interpretation (in the original version due to Bohr and Heisenberg), which the author relates to the mathematical formalism of operator algebras originally created by von Neumann. The book therefore includes comprehensive appendices on functional analysis and C*-algebras, as well as a briefer one on logic, category theory, and topos theory. Matters of foundational as well as mathematical interest that are covered in detail include symmetry (and its "spontaneous" breaking), the measurement problem, the Kochen-Specker, Free Will, and Bell Theorems, the Kadison-Singer conjecture, quantization, indistinguishable particles, the quantum theory of large systems, and quantum logic, the latter in connection with the topos approach to quantum theory. This book is Open Access under a CC BY licence.