This pioneering book addresses the question: Are the standard procedures of canonical quantization fully satisfactory, or is there more to learn about assigning a proper quantum system to a given classical system? As shown in this book, the answer to this question is: The standard procedures of canonical quantization are not the whole story!This book offers alternative quantization procedures that complete the story of quantization. The initial chapters are designed to present the new procedures in a clear and simple manner for general readers. As is necessary, systems that exhibit acceptable results with conventional quantization lead to the same results when the new procedures are used for them. However, later chapters examine selected models that lead to unacceptable results when quantized conventionally. Fortunately, these same models lead to acceptable results when the new quantization procedures are used.

Italian researchers involved in different aspects of the foundations and history of quantum mechanics are brought together in an interdisciplinary debate in this text. The book presents an overview of the state of Italian work in the field and of the open problems that still exist in the foundations of the theory. Physicists, logicians, mathematicians and epistemologists whose research concerns the historical analysis of quantum mechanics may find this text to be useful reading.

This concise, accessible text provides a thorough introduction to quantum computing - an exciting emergent field at the interface of the computer, engineering, mathematical and physical sciences. Aimed at advanced undergraduate and beginning graduate students in these disciplines, the text is
technically detailed and is clearly illustrated throughout with diagrams and exercises. Some prior knowledge of linear algebra is assumed, including vector spaces and inner products. However, prior familiarity with topics such as tensor products and spectral decomposition is not required, as the
necessary material is reviewed in the text.

By covering theory, design, and fabrication of nanostructured superconducting materials, this monograph is an invaluable resource for research and development. Examples are energy saving solutions, healthcare, and communication technologies. Key ingredients are nanopatterned materials which help to improve the superconducting critical parameters and performance of superconducting devices, and lead to novel functionalities. Contents Tutorial on nanostructured superconductors Imaging vortices in superconductors: from the atomic scale to macroscopic distances Probing vortex dynamics on a single vortex level by scanning ac-susceptibility microscopy STM studies of vortex cores in strongly confined nanoscale superconductors Type-1.5 superconductivity Direct visualization of vortex patterns in superconductors with competing vortex-vortex interactions Vortex dynamics in nanofabricated chemical solution deposition high-temperature superconducting films Artificial pinning sites and their applications Vortices at microwave frequencies Physics and operation of superconducting single-photon devices Josephson and charging effect in mesoscopic superconducting devices NanoSQUIDs: Basics & recent advances Bi2Sr2CaCu2O8 intrinsic Josephson junction stacks as emitters of terahertz radiation| Interference phenomena in superconductor-ferromagnet hybrids Spin-orbit interactions, spin currents, and magnetization dynamics in superconductor/ferromagnet hybrids Superconductor/ferromagnet hybrids

The topics of this book are the mathematical foundations of non-relativistic quantum mechanics and the mathematical theory they require. The main characteristic of the book is that the mathematics is developed assuming familiarity with elementary analysis only. Moreover, all the proofs are carried out in detail. These features make the book easily accessible to readers with only the mathematical training offered by undergraduate education in mathematics or in physics, and also ideal for individual study. The principles of quantum mechanics are discussed with complete mathematical accuracy and an effort is made to always trace them back to the experimental reality that lies at their root. The treatment of quantum mechanics is axiomatic, with definitions followed by propositions proved in a mathematical fashion. No previous knowledge of quantum mechanics is required. This book is designed so that parts of it can be easily used for various courses in mathematics and mathematical physics, as suggested in the Preface.The book is of interest to researchers and graduate students in functional analysis, who can see how closely an important part of their chosen field is linked with quantum mechanics, and also to physicists, who can see how the abstract language of functional analysis brings unity to the apparently distinct approaches employed in quantum theory.

During its forty year lifespan, string theory has always had the power to divide, being called both a 'theory of everything' and a 'theory of nothing'. Critics have even questioned whether it qualifies as a scientific theory at all. This book adopts an objective stance, standing back from the question of the truth or falsity of string theory and instead focusing on how it came to be and how it came to occupy its present position in physics. An unexpectedly rich history is revealed, with deep connections to our most well-established physical theories. Fully self-contained and written in a lively fashion, the book will appeal to a wide variety of readers from novice to specialist.

This book attempts to explain the core of physics, the origin of everything and anything. It explains why physics at the most fundamental level, and especially quantum mechanics, has moved away from naive realism towards abstraction, and how this means that we can begin to answer some of the most fundamental questions which trouble us all, about space, time, matter, etc. It provides an original approach based on symmetry which will be of interest to professionals as well as lay people.In the book, virtually no prior knowledge is assumed, but the readers are allowed to participate in a discussion of very deep ideas. Throughout the book, the readers are guided through some important ideas which need to be explained mathematically. The key fact is that the mathematics is not about calculation but about concepts. Much of it can be simplified using coloured text and diagrams. This means that ideas which are important to everyone who wants to know how the universe is structured are not glossed over as being too difficult for anybody but the experts.This book is written for a wide audience. Experts will gain a great deal, but so will lay readers. This would be an ideal book for students to read before progressing to another book by the author, The Foundations of Physical Law.

This captivating book presents a new, unified picture of the everyday world around us. It provides rational, scientific support for the idea that there may well be more to our reality than meets the eye...Accessible and engaging for readers with no prior knowledge of quantum physics, author Ruth Kastner draws on the popular transactional interpretation of quantum mechanics to explain our 'quantum reality.' Her book focuses on modern-day examples and deals with big philosophical questions as well as ideas from physics.If you have any interest in quantum physics, this book is for you - whether you be a physics student or academic, or simply an inquisitive reader who wants to delve deeper into the reality of the world around you. Dr Ruth Kastner has received two National Science Foundation awards for the study of interpretational issues in quantum theory.

Covers the State of the Art in Superfluidity and Superconductivity Superfluid States of Matter addresses the phenomenon of superfluidity/superconductivity through an emergent, topologically protected constant of motion and covers topics developed over the past 20 years. The approach is based on the idea of separating universal classical-field superfluid properties of matter from the underlying system's "quanta." The text begins by deriving the general physical principles behind superfluidity/superconductivity within the classical-field framework and provides a deep understanding of all key aspects in terms of the dynamics and statistics of a classical-field system. It proceeds by explaining how this framework emerges in realistic quantum systems, with examples that include liquid helium, high-temperature superconductors, ultra-cold atomic bosons and fermions, and nuclear matter. The book also offers several powerful modern approaches to the subject, such as functional and path integrals. Comprised of 15 chapters, this text: Establishes the fundamental macroscopic properties of superfluids and superconductors within the paradigm of the classical matter field Deals with a single-component neutral matter field Considers fundamentals and properties of superconductors Describes new physics of superfluidity and superconductivity that arises in multicomponent systems Presents the quantum-field perspective on the conditions under which classical-field description is relevant in bosonic and fermionic systems Introduces the path integral formalism Shows how Feynman path integrals can be efficiently simulated with the worm algorithm Explains why nonsuperfluid (insulating) ground states of regular and disordered bosons occur under appropriate conditions Explores superfluid solids (supersolids) Discusses the rich dynamics of vortices and various aspects of superfluid turbulence at T 0 Provides account of BCS theory for the weakly interacting Fermi gas Highlights and analyzes the most crucial developments that has led to the current understanding of superfluidity and superconductivity Reviews the variety of superfluid and superconducting systems available today in nature and the laboratory, as well as the states that experimental realization is currently actively pursuing

This book discusses the main concepts of the Standard Model of elementary particles in a compact and straightforward way. The theoretical results are derived using the physical phenomena as a starting point. This inductive approach allows a deep understanding of the methods used for solving problems in this field. This second, revised edition is expanded with biographical notes contextualizing the main results in quantum field theory.

All modern books on Einstein emphasize the genius of his relativity theory and the corresponding corrections and extensions of the ancient space-time concept. However, Einstein s opposition to the use of probability in the laws of nature and particularly in the laws of quantum mechanics is criticized and often portrayed as outdated.

The author of Einstein Was Right takes a different view and shows that Einstein created a "Trojan horse" ready to unleash forces against the use of probability as a basis for the laws of nature. Einstein warned that the use of probability would, in the final analysis, lead to "spooky" actions and mysterious instantaneous influences at a distance.

John Bell pulled Einstein s Trojan horse into the castle of physics. He developed a theory that, together with experimental results of Aspect, Zeilinger, and others, "proves" the existence of quantum non-localities, instantaneous influences. These have indeed the nature of what Einstein labeled as "spooky."

The book Einstein Was Right shows that Bell was not aware of the special role that time and space-time play in any rigorous probability theory. As a consequence, his formalism is not general enough to be applied to the Aspect-Zeilinger type of experiments and his conclusions about the existence of instantaneous influences at a distance are incorrect.

This fact suggests a world view that is less optimistic about claims that teleportation and influences at a distance could open new horizons and provide the possibility of quantum computing. On the positive side, however, and as compensation, we are assured that the space-time picture of mankind developed over millions of years and perfected by Einstein, is still able to cope with the phenomena that nature presents us on the atomic and sub-atomic level and that the "quantum weirdness" may be explainable and understandable after all. "

This book attempts to explain the core of physics, the origin of everything and anything. It explains why physics at the most fundamental level, and especially quantum mechanics, has moved away from naive realism towards abstraction, and how this means that we can begin to answer some of the most fundamental questions which trouble us all, about space, time, matter, etc. It provides an original approach based on symmetry which will be of interest to professionals as well as lay people.In the book, virtually no prior knowledge is assumed, but the readers are allowed to participate in a discussion of very deep ideas. Throughout the book, the readers are guided through some important ideas which need to be explained mathematically. The key fact is that the mathematics is not about calculation but about concepts. Much of it can be simplified using coloured text and diagrams. This means that ideas which are important to everyone who wants to know how the universe is structured are not glossed over as being too difficult for anybody but the experts.This book is written for a wide audience. Experts will gain a great deal, but so will lay readers. This would be an ideal book for students to read before progressing to another book by the author, The Foundations of Physical Law.

Quantum phenomena of many-particle systems are fascinating in their complexity and are consequently not fully understood and largely untapped in terms of practical applications. Ultracold gases provide a unique platform to build up model systems of quantum many-body physics with highly controlled microscopic constituents. In this way, many-body quantum phenomena can be investigated with an unprecedented level of precision, and control and models that cannot be solved with present day computers may be studied using ultracold gases as a quantum simulator.This book addresses the need for a comprehensive description of the most important advanced experimental methods and techniques that have been developed along with the theoretical framework in a clear and applicable format. The focus is on methods that are especially crucial in probing and understanding the many-body nature of the quantum phenomena in ultracold gases and most topics are covered both from a theoretical and experimental viewpoint, with interrelated chapters written by experts from both sides of research.Graduate students and post-doctoral researches working on ultracold gases will benefit from this book, as well as researchers from other fields who wish to gain an overview of the recent fascinating developments in this very dynamically evolving field. Sufficient level of both detailed high level research and a pedagogical approach is maintained throughout the book so as to be of value to those entering the field as well as advanced researchers. Furthermore, both experimentalists and theorists will benefit from the book; close collaboration between the two are continuously driving the field to a very high level and will be strengthened to continue the important progress yet to be made in the field.

Although there are many textbooks that deal with the formal apparatus of quantum mechanics (QM) and its application to standard problems, none take into account the developments in the foundations of the subject which have taken place in the last few decades. There are specialized treatises on various aspects of the foundations of QM, but none that integrate those topics with the standard material. This book aims to remove that unfortunate dichotomy, which has divorced the practical aspects of the subject from the interpretation and broader implications of the theory.In this edition a new chapter on quantum information is added. As the topic is still in a state of rapid development, a comprehensive treatment is not feasible. The emphasis is on the fundamental principles and some key applications, including quantum cryptography, teleportation of states, and quantum computing. The impact of quantum information theory on the foundations of quantum mechanics is discussed. In addition, there are minor revisions to several chapters.The book is intended primarily as a graduate level textbook, but it will also be of interest to physicists and philosophers who study the foundations of QM. Parts of it can be used by senior undergraduates too.

Although there are many textbooks that deal with the formal apparatus of quantum mechanics (QM) and its application to standard problems, none take into account the developments in the foundations of the subject which have taken place in the last few decades. There are specialized treatises on various aspects of the foundations of QM, but none that integrate those topics with the standard material. This book aims to remove that unfortunate dichotomy, which has divorced the practical aspects of the subject from the interpretation and broader implications of the theory.In this edition a new chapter on quantum information is added. As the topic is still in a state of rapid development, a comprehensive treatment is not feasible. The emphasis is on the fundamental principles and some key applications, including quantum cryptography, teleportation of states, and quantum computing. The impact of quantum information theory on the foundations of quantum mechanics is discussed. In addition, there are minor revisions to several chapters.The book is intended primarily as a graduate level textbook, but it will also be of interest to physicists and philosophers who study the foundations of QM. Parts of it can be used by senior undergraduates too.

The book originated in a series of lectures given at Liverpool in 2013 to a group that included postgraduate and undergraduate students and staff of the Physics Department. They followed from two very successful lectures given to the undergraduate Physical Society. It seemed that there was a very large interest among the students in investigating the foundations of physics in a way that was never done in physics courses, and was not available in books or other outlets. However, the idea was to create a framework in which students (and interested staff) could develop their own thinking relative to the ideas in the lectures. So it was important to create both conceptual and mathematical structures on the issues that are important at this level. The book has the right sort of technical content to allow for this development, but doesn't lose itself in excessive details. The ideal use for this book would be on postgraduate courses where students would be encouraged to think about the foundations in a way that is well beyond the superficial. However, a course on aspects of this material would also be valuable at the undergraduate level, where students could be stimulated into believing that creative thinking could solve the problems that emerge when we confront foundational problems.

Our understanding of the physical world was revolutionized in the twentieth century - the era of "modern physics". Two books by the second author entitled Introduction to Modern Physics: Theoretical Foundations and Advanced Modern Physics: Theoretical Foundations, aimed at the very best students, present the foundations and frontiers of today's physics. Many problems are included in these texts. A previous book by the current authors provides solutions to the over 175 problems in the first volume.A third volume Topics in Modern Physics: Theoretical Foundations has recently appeared, which covers several subjects omitted in the essentially linear progression in the previous two. This book has three parts: part 1 is on quantum mechanics, part 2 is on applications of quantum mechanics, and part 3 covers some selected topics in relativistic quantum field theory. Parts 1 and 2 follow naturally from the initial volume. The present book provides solutions to the over 135 problems in this third volume.The three volumes in this series, together with the solutions manuals, provide a clear, logical, self-contained, and comprehensive base from which students can learn modern physics. When finished, readers should have an elementary working knowledge in the principal areas of theoretical physics of the twentieth century.

In this book we have solved the complicated problem of constructing upper bounds for many-time averages for the case of a fairly broad class of model systems with four-fermion interaction. The methods proposed in this book for solving this problem will undoubtedly find application not only for the model systems associated with the theory of superconductivity considered here. The theoretical methods developed in Chapters 1 and 2 are already applicable to a much broader class of model systems from statistical physics and the theory of elementary particles.

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.

This thesis is devoted to the systematic study of non-local theories that respect Lorentz invariance and are devoid of new, unphysical degrees of freedom. Such theories are attractive for phenomenological applications since they are mostly unconstrained by current experiments. Non-locality has played an increasingly important role in the physics of the last decades, appearing in effective actions in quantum field theory, and arising naturally in string theory and non-commutative geometry. It may even be a necessary ingredient for quantum theories of gravity. It is a feature of quantum entanglement, and may even solve the long-standing black hole information loss problem. "Non-locality" is a broad concept with many promising and fruitful applications in theoretical and mathematical physics. After a historical and pedagogical introduction into the concept of non-locality the author develops the notion of non-local Green functions to study various non-local weak-field problems in quantum mechanics, quantum field theory, gravity, and quantum field theory in curved spacetime. This thesis fills a gap in the literature by providing a self-contained exploration of weak-field effects in non-local theories, thereby establishing a "non-local intuition" which may serve as a stepping stone for studies of the full, non-linear problem of non-locality.

Inverse problems in wave propagation occur in geophysics, ocean acoustics, civil and environmental engineering, ultrasonic non-destructive testing, biomedical ultrasonics, radar, astrophysics, as well as other areas of science and technology. The papers in this volume cover these scientific and technical topics, together with fundamental mathematical investigations of the relation between waves and scatterers.

Starting with numerical algorithms resulting in new kinds of amazing fractal patterns on the sphere, this book describes the theory underlying these phenomena and indicates possible future applications. The book also explores the following questions:

Organisms endowed with life show a sense of awareness, interacting with and learning from the universe in and around them. Each level of interaction involves transfer of information of various kinds, and at different levels. Each thread of information is interlinked with the other, and woven together, these constitute the universe - both the internal self and the external world - as we perceive it. They are, figuratively speaking, Nature's longest threads. This volume reports inter-disciplinary research and views on information and its transfer at different levels of organization by reputed scientists working on the frontier areas of science. It is a frontier where physics, mathematics and biology merge seamlessly, binding together specialized streams such as quantum mechanics, dynamical systems theory, and mathematics. The topics would interest a broad cross-section of researchers in life sciences, physics, cognition, neuroscience, mathematics and computer science, as well as interested amateurs, familiarizing them with frontier research on understanding information transfer in living systems.

Among the most fascinating and rapidly developing areas in modem physics is the study of cosmological phenomena such as black holes, the cosmic microwave background, and the inflationary nature of the universe. Recent theoretical and experimental developments in these fields have significantly increased our understanding of these exciting and important topics. In order to allow the reader fully to understand these new developments, Quantum Theory, Black Holes and Inflation begins by introducing the theory of quantised fields in a mathematically rigorous fashion. Concentrating on the path integral approach to quantum field theory, the essential mathematical tools are developed to allow the reader to get to grips with the ways in which the theory has been successfully applied to a number of areas in modern cosmology. The second half of Quantum Theory, Black Holes and Inflation explains a number of the most successful applications to date, including the theory of black hole evaporation and thermodynamics, and the theory of quantum effects in the inflationary model of the universe.

Quantum Theory, Black Holes and Inflation will be of great interest to all those involved in these vibrant areas of research. Its combination of mathematical background and the most successful modern applications of the theory make it accessible and interesting to both postgraduate students and more experienced researchers in the field.