This is a book presenting to a wide audience of readers, ranging from fans of science to professional researchers, some of the authors' recent discoveries in three distinct, but intimately related domains: probability theory (Bertrand's paradox), observation in physics (the measurement problem) and the modeling of experiments in psychology (quantum cognition). In all three of these domains of investigation, and the associated problems, the authors explain how to advantageously use the key notion of universal measurement, which constitutes the fil rouge of the whole text.

This book provides an in-depth and rigorous study of the Wigner transform and its variants. They are presented first within a context of a general mathematical framework, and then through applications to quantum mechanics. The Wigner transform was introduced by Eugene Wigner in 1932 as a probability quasi-distribution which allows expression of quantum mechanical expectation values in the same form as the averages of classical statistical mechanics. It is also used in signal processing as a transform in time-frequency analysis, closely related to the windowed Gabor transform.Written for advanced-level students and professors in mathematics and mathematical physics, it is designed as a complete textbook course providing analysis on the most important research on the subject to date. Due to the advanced nature of the content, it is also suitable for research mathematicians, engineers and chemists active in the field.

This book provides an in-depth and rigorous study of the Wigner transform and its variants. They are presented first within a context of a general mathematical framework, and then through applications to quantum mechanics. The Wigner transform was introduced by Eugene Wigner in 1932 as a probability quasi-distribution which allows expression of quantum mechanical expectation values in the same form as the averages of classical statistical mechanics. It is also used in signal processing as a transform in time-frequency analysis, closely related to the windowed Gabor transform.Written for advanced-level students and professors in mathematics and mathematical physics, it is designed as a complete textbook course providing analysis on the most important research on the subject to date. Due to the advanced nature of the content, it is also suitable for research mathematicians, engineers and chemists active in the field.

Causal Physics: Photons by Non Interactions of Waves redefines the mathematical Superposition Principle as an operational Superposition Effect; which is the measurable physical transformation experienced by a detector due to stimulations induced by multiple waves simultaneously acting on the detecting dipoles. This light-matter interaction process driven model emerges naturally by incorporating the observed properties, Non-Interaction of Waves (NIW) and quantized photo detectors needing to fill up their "quantum-cups" with the required quantity of energy from all the stimulating waves around it. By not incorporating this NIW-property explicitly, quantum mechanics failed to extract various embedded realities in the theory while incorporated unnecessary hypotheses like wave-particle duality. The book utilizes this NIW-property to explain all the major optical phenomena (diffraction, spectrometry, coherence.) without using any self-contradictory hypotheses that are prevalent now. The book redefines the old ether (constituting the space) as a stationary Complex Tension Field (CTF), holding all the energy of the universe (no need for Dark Energy of Dark Matter). CTF sustains perpetually propagating EM waves as its linear excitations and the particles as self-looped localized resonant non-linear excitations. Tensions are identified by Maxwell, then the velocities of emitting and detecting atoms through the CTF contribute to the Doppler shifts separately. This calls for re-visiting physical processes behind Hubble Redshift and hence Expanding Universe. The success of the book derives from a novel thinking strategy of visualizing the invisible interaction processes, named as Interaction Process Mapping Epistemology (IPM-E). This is over and above the prevailing strategy of Measurable Data Modeling Epistemology (MDM-E). The approach inspires the next generation of physicists to recognizing that the "foundation of the edifice of physics" has not yet been finalized. IPM-E will stimulate more of us to become technology innovators by learning to emulate the ontologically real physical processes in nature and become more evolution congruent. Critical thinkers without expertise in optical science and engineering, will appreciate the value of the content by reading the book backward, starting from Ch.12; which explains the critical thinking methodology besides giving a very brief summary of the contents in the previous chapters. Establishes that abandoning the wave-particle-duality actually allows us to extract more realities out of quantum mechanics. Illustrates how the discovery of the NIW-property profoundly impacts several branches of fundamental physics, including Doppler effect and hence the cosmological red shift Summarizes that many ad hoc hypotheses from physics can be removed, a la Occam's razor, while improving the reality and comprehension of some of the current working theories Demonstrates that our persistent attempts to restore causality in physical theories will be guided by our capability to visualize the invisible light matter interaction processes that are behind the emergence of all measurable data Draws close attention to the invisible but ontological interaction processes behind various optical phenomena so we can emulate them more efficiently and knowledgably in spite of limitations of our theories Designed as a reference book for general physics and philosophy, this optical science and engineering book is an ideal resource for optical engineers, physicists, and those working with modern optical equipment and high precision instrumentation.

Light and Vacuum presents a synthesis of selected fundamental topics of electromagnetic wave theory and quantum electrodynamics (QED) and analyzes the main theoretical difficulties encountered to ensure a coherent mathematical description of the simultaneous wave-particle nature of light, put in evidence by the experiments. The notion and the role of the quantum vacuum, strongly related to light, are extensively investigated.Classical electrodynamics issued from Maxwell's equations revealed the necessity of introducing the notion of volume for an electromagnetic wave to stand entailing precise values of cut-off wavelengths to account for the shape and dimensions of the surrounding space. Conversely, in QED, light is considered to be composed of point particles disregarding the conceptual question on how the frequency of oscillating electric and magnetic fields may be attributed to a point particle.To conciliate these concepts, the book provides a comprehensive overview of the author's work, including innovative contributions on the quantization of the vector potential amplitude at a single photon state, the non-local simultaneous wave-particle mathematical representation of the photon and finally the quantum vacuum. The purpose of the advanced elaborations is to raise questions, give hints and answers, and finally aspire for further theoretical and experimental studies in order to improve our knowledge and understanding on the real essence of Light and Vacuum.In this new edition, improvements have been made to the various chapters taking into account the actual status of the knowledge in this field. The photon wave function is further analyzed and a new concept of quantum vacuum is advanced compatible with recent astrophysical observations.

Dissipative forces play an important role in problems of classical as well as quantum mechanics. Since these forces are not among the basic forces of nature, it is essential to consider whether they should be treated as phenomenological interactions used in the equations of motion, or they should be derived from other conservative forces. In this book we discuss both approaches in detail starting with the Stoke's law of motion in a viscous fluid and ending with a rather detailed review of the recent attempts to understand the nature of the drag forces originating from the motion of a plane or a sphere in vacuum caused by the variations in the zero-point energy. In the classical formulation, mathematical techniques for construction of Lagrangian and Hamiltonian for the variational formulation of non-conservative systems are discussed at length. Various physical systems of interest including the problem of radiating electron, theory of natural line width, spin-boson problem, scattering and trapping of heavy ions and optical potential models of nuclear reactions are considered and solved.

Dissipative forces play an important role in problems of classical as well as quantum mechanics. Since these forces are not among the basic forces of nature, it is essential to consider whether they should be treated as phenomenological interactions used in the equations of motion, or they should be derived from other conservative forces. In this book we discuss both approaches in detail starting with the Stoke's law of motion in a viscous fluid and ending with a rather detailed review of the recent attempts to understand the nature of the drag forces originating from the motion of a plane or a sphere in vacuum caused by the variations in the zero-point energy. In the classical formulation, mathematical techniques for construction of Lagrangian and Hamiltonian for the variational formulation of non-conservative systems are discussed at length. Various physical systems of interest including the problem of radiating electron, theory of natural line width, spin-boson problem, scattering and trapping of heavy ions and optical potential models of nuclear reactions are considered and solved.

This book provides a comprehensive view of the contemporary methods for quantum-light engineering. In particular, it addresses different technological branches and therefore allows the reader to quickly identify the best technology - application match. Non-classical light is a versatile tool, proven to be an intrinsic part of various quantum technologies. Its historical significance has made it the subject of many text books written both from theoretical and experimental point of view. This book takes another perspective by giving an insight to modern technologies used to generate and manipulate quantum light.

This book presents the author's personal historical perspective and conceptual analysis on symmetry and geometry. The author enlightens with modern views the historical process which led to the contemporary vision of space and symmetry that are used in theoretical physics and in particular in such abstract and advanced descriptions of the physical world as those provided by supergravity. The book is written intertwining storytelling and philosophical argumentation with some essential technical material. The author argues that symmetry and geometry are inextricably entangled and their current meaning is the result of a long process of abstraction which was determined through history and can be understood within the analytic system of thought of western civilization that started with the Ancient Greeks. The evolution of geometry and symmetry theory in the last forty years has been deeply and constructively influenced by supersymmetry/supergravity and the allied constructions of strings and branes. Further advances in theoretical physics cannot be based simply on the Galilean method of interrogating nature and then formulating a testable theory to explain the observed phenomena. One ought to interrogate human thought, meaning frontier-line mathematics concerned with geometry and symmetry in order to find there the threads of so far unobserved correspondences, reinterpretations and renewed conceptions.

Unravels Complex Problems through Quantum Monte Carlo Methods Clusters hold the key to our understanding of intermolecular forces and how these affect the physical properties of bulk condensed matter. They can be found in a multitude of important applications, including novel fuel materials, atmospheric chemistry, semiconductors, nanotechnology, and computational biology. Focusing on the class of weakly bound substances known as van derWaals clusters or complexes, Stochastic Simulations of Clusters: Quantum Methods in Flat and Curved Spaces presents advanced quantum simulation techniques for condensed matter. The book develops finite temperature statistical simulation tools and real-time algorithms for the exact solution of the Schroedinger equation. It draws on potential energy models to gain insight into the behavior of minima and transition states. Using Monte Carlo methods as well as ground state variational and diffusion Monte Carlo (DMC) simulations, the author explains how to obtain temperature and quantum effects. He also shows how the path integral approach enables the study of quantum effects at finite temperatures. To overcome timescale problems, this book supplies efficient and accurate methods, such as diagonalization techniques, differential geometry, the path integral method in statistical mechanics, and the DMC approach. Gleaning valuable information from recent research in this area, it presents special techniques for accelerating the convergence of quantum Monte Carlo methods.

Have you ever puzzled over how to perform Boolean logic at the atomic scale? Or wondered how you can carry out more general calculations in one single molecule or using a surface dangling bond atomic scale circuit? This volume gives you an update on the design of single molecule devices, such as recitfiers, switches and transistors, more advanced semi-classical and quantum boolean gates integrated in a single molecule or constructed atom by atom on a passivated semi-conductor surface and describes their interconnections with adapted nano-scale wiring. The main contributors to the field of single molecule logic gates and surface dangling bond atomic scale circuits theory and design, were brought together for the first time to contribute on topics such as molecule circuits, surface dangling bond circuits, quantum controlled logic gates and molecular qubits. Contributions in this volume originate from the Barcelona workshop of the AtMol conference series, held from January 12-13 2012.

'All are every interesting topics treated with a high level of mathematical sophistication. One of the very useful tricks the author repeatedly resorts to is the introduction of one-parameter families of operators interpolating between two operators which appear naturally in the formalism. From this one-parameter family a differential equation for the determinant (or ratio of determinants) or for correlation functions is derived, which can then be solved. This is a very simple, elegant and powerful technique.'Mathematical Reviews ClippingsFunctional Integrals is a well-established method in mathematical physics, especially those mathematical methods used in modern non-perturbative quantum field theory and string theory. This book presents a unique, original and modern treatment of strings representations on Bosonic Quantum Chromodynamics and Bosonization theory on 2d Gauge Field Models, besides of rigorous mathematical studies on the analytical regularization scheme on Euclidean quantum field path integrals and stochastic quantum field theory. It follows an analytic approach based on Loop space techniques, functional determinant exact evaluations and exactly solubility of four dimensional QCD loop wave equations through Elfin Botelho fermionic extrinsic self avoiding string path integrals.

This breakthrough volume touts having dissolved the remaining barriers to implementing Bulk Universal Quantum Computing (UQC), and as such most likely describes the most advanced QC development platform. Numerous books, hundreds of patents, thousands of papers and a Googolplex of considerations fill the pantheon of QC R&D. Of late QC mathemagicians claim QCs already exist; but by what chimeric definition. Does flipping a few qubits in a logic gate without an algorithm qualify as quantum computing? In physics, theory bears little weight without rigorous experimental confirmation, less if new, radical or a paradigm shift. This volume develops quantum computing based on '3rd regime' physics of Unified Field Mechanics (UFM). What distinguishes this work from a myriad of other avenues to UQC under study? Virtually all R&D paths struggle with technology and decoherence. If highly favored room-sized cryogenically cooled QCs ever become successful, they would be reminiscent of the city block-sized Eniac computer of 1946. The QC prototype proposed herein is room temperature and tabletop. It is dramatically different in that it is not confined to the limitations of quantum mechanics; since it is based on principles of UFM the Uncertainty Principle and Decoherence no longer apply. Thus this QC model could be implemented on any other quantum platform!

This thesis discusses searches for electroweakly produced supersymmetric partners of the gauge and the Higgs bosons (gauginos and higgsinos) decaying to multiple leptons, using pp collisions at sqrt(s) = 13 TeV. The thesis presents an in-depth study of multiple searches, as well as the first 13 TeV cross section measurement for the dominant background in these searches, WZ production. Two searches were performed using 36.1/fb of data: the gaugino search, which makes use of a novel kinematic variable, and the higgsino search, which produced the first higgsino limits at the LHC. A search using 139/fb of data makes use of a new technique developed in this thesis to cross check an excess of data above the background expectation in a search using a Recursive Jigsaw Reconstruction technique. None of the searches showed a significant excess of data, and limits were expanded with respect to previous results. These searches will benefit from the addition of luminosity during HL-LHC; however, the current detector will not be able to withstand the increase in radiation. Electronics for the detector upgrade are tested and irradiated to ensure their performance.

This volume goes beyond the understanding of symmetries and exploits them in the study of the behavior of both classical and quantum physical systems. Thus it is important to study the symmetries described by continuous (Lie) groups of transformations. We then discuss how we get operators that form a Lie algebra. Of particular interest to physics is the representation of the elements of the algebra and the group in terms of matrices and, in particular, the irreducible representations. These representations can be identified with physical observables.This leads to the study of the classical Lie algebras, associated with unitary, unimodular, orthogonal and symplectic transformations. We also discuss some special algebras in some detail. The discussion proceeds along the lines of the Cartan-Weyl theory via the root vectors and root diagrams and, in particular, the Dynkin representation of the roots. Thus the representations are expressed in terms of weights, which are generated by the application of the elements of the algebra on uniquely specified highest weight states. Alternatively these representations can be described in terms of tensors labeled by the Young tableaux associated with the discrete symmetry Sn. The connection between the Young tableaux and the Dynkin weights is also discussed. It is also shown that in many physical systems the quantum numbers needed to specify the physical states involve not only the highest symmetry but also a number of sub-symmetries contained in them. This leads to the study of the role of subalgebras and in particular the possible maximal subalgebras. In many applications the physical system can be considered as composed of subsystems obeying a given symmetry. In such cases the reduction of the Kronecker product of irreducible representations of classical and special algebras becomes relevant and is discussed in some detail. The method of obtaining the relevant Clebsch-Gordan (C-G) coefficients for such algebras is discussed and some relevant algorithms are provided. In some simple cases suitable numerical tables of C-G are also included.The above exposition contains many examples, both as illustrations of the main ideas as well as well motivated applications. To this end two appendices of 51 pages - 11 tables in Appendix A, summarizing the material discussed in the main text and 39 tables in Appendix B containing results of more sophisticated examples are supplied. Reference to the tables is given in the main text and a guide to the appropriate section of the main text is given in the tables.

This book offers a concise and up-to-date introduction to the popular field of quantum information. It has originated in a series of invited lecture courses at various universities in different countries. This is reflected in its informal style of exposition and presentation of key results in the subject. In addition to treating quantum communication, entanglement and algorithms in great depth, this book also addresses a number of interesting miscellaneous topics, such as Maxwell's demon, Landauer's erasure, the Bekenstein bound and Caratheodory's treatment of the Second law of thermodyanmics. All mathematical derivations are based on clear physical pictures which make even the most involved results - such as the Holevo bound - look comprehensible and transparent. The book is ideal as a first introduction to the subject, but may also appeal to the specialist due to its unique presentation.

This volume is a compilation of lectures delivered at the TASI 2015 summer school, 'New Frontiers in Fields and Strings', held at the University of Colorado Boulder in June 2015. The school focused on topics in theoretical physics of interest to contemporary researchers in quantum field theory and string theory. The lectures are accessible to graduate students in the initial stages of their research careers.

Symmetries play a fundamental role in physics. Non-Abelian gauge symmetries are the symmetries behind theories for massless spin-1 particles, while the reparametrization symmetry is behind Einstein's gravity theory for massless spin-2 particles. In supersymmetric theories these particles can be connected also to massless fermionic particles. Does Nature stop at spin-2 or can there also be massless higher spin theories. In the past strong indications have been given that such theories do not exist. However, in recent times ways to evade those constraints have been found and higher spin gauge theories have been constructed. With the advent of the AdS/CFT duality correspondence even stronger indications have been given that higher spin gauge theories play an important role in fundamental physics.All these issues were discussed at a recent international workshop in Singapore where the leading scientists in the field participated. This volume presents an up-to-date, detailed overview of the theories including its historic background, as well as the latest accomplishments in understanding the foundational properties of higher spin physics.

Proceedings of the International School of Subnuclear Physics, ISSP 2014, 52nd Course, ERICE, Erice, 24 June - 3 July 2014.

The second edition of this book deals, as the first, with the foundations of classical physics from the 'symplectic' point of view, and of quantum mechanics from the 'metaplectic' point of view. We have revised and augmented the topics studied in the first edition in the light of new results, and added several new sections. The Bohmian interpretation of quantum mechanics is discussed in detail. Phase space quantization is achieved using the 'principle of the symplectic camel', which is a deep topological property of Hamiltonian flows. We introduce the notion of 'quantum blob', which can be viewed as the fundamental phase space unit. The mathematical tools developed in this book are the theory of the symplectic and metaplectic group, the Maslov index in a rigorous form, and the Leray index of a pair of Lagrangian planes. The concept of the 'metatron' is introduced, in connection with the Bohmian theory of motion. The short-time behavior of the propagator is studied and applied to the quantum Zeno effect.

The structural aspects of composite quantum systems in the foundation, interpretation and application of quantum theory is an increasingly prominent topic of physics research. As an emerging field, it seeks to understand the origins of the classical world of experience from the quantum level.Quantum Structural Studies presents conceptual fundamentals and mathematical methods for investigating the structuring of quantum systems into subsystems. Split into four sections, the topics covered include the historical and philosophical aspects of quantum structures, specific interpretive approaches and ontologies, and alternative methodological approaches to quantum mechanics. Questions addressed are: Specialists, graduate students and researchers seeking an introduction to the field of emergent structures and new directions for research and experimentation can use this book to find up-to-date representative texts and reviews.

The application of quantum mechanics to many-particle systems has been an active area of research in recent years as researchers have looked for ways to tackle difficult problems in this area. The quantum trajectory method provides an efficient computational technique for solving both stationary and time-evolving states, encompassing a large area of quantum mechanics. Quantum Trajectories brings the expertise of an international panel of experts who focus on the epistemological significance of quantum mechanics through the quantum theory of motion. Emphasizing a classical interpretation of quantum mechanics as developed by de Broeglie and Bohm, this volume: Introduces the concept of the quantum theory of motion Explains the connection with conventional quantum mechanics Presents various numerical techniques generated from the Bohmian approach Describes the epistemological significance of quantum trajectories Provides an authoritative account of the foundations of quantum mechanics vis-a-vis that of the Bohmian mechanics The popularity of using the quantum trajectory as a computational tool has exploded over the last decade, finally bringing this methodology to the level of practical applications. Many of the experts in the field who have either developed the methodology or have improved upon it have contributed chapters to this volume, making it a state-of-the-art expression of the field as it exists today and providing insight into the future of this technology.

This textbook offers a clear and comprehensive introduction to methods and applications in quantum mechanics, one of the core components of undergraduate physics courses. It follows on naturally from the previous volumes in this series, thus developing the understanding of quantized states further on. The first part of the book introduces the quantum theory of angular momentum and approximation methods. More complex themes are covered in the second part of the book, which describes multiple particle systems and scattering theory. Ideally suited to undergraduate students with some grounding in the basics of quantum mechanics, the book is enhanced throughout with learning features such as boxed inserts and chapter summaries, with key mathematical derivations highlighted to aid understanding. The text is supported by numerous worked examples and end of chapter problem sets. About the Theoretical Physics series Translated from the renowned and highly successful German editions, the eight volumes of this series cover the complete core curriculum of theoretical physics at undergraduate level. Each volume is self-contained and provides all the material necessary for the individual course topic. Numerous problems with detailed solutions support a deeper understanding. Wolfgang Nolting is famous for his refined didactical style and has been referred to as the "German Feynman" in reviews.

The matter in our universe is composed of electrons and quarks. The dynamics of electrons and quarks is described by the Standard Model of particle physics, which is based on quantum field theories. The general framework of quantum field theories is described in this book. After the classical mechanics and the relativistic mechanics the details of classical scalar fields, of electrodynamics and of quantum mechanics are discussed. Then the quantization of scalar fields, of spinor fields and of vector fields is described.The basic interactions are described by gauge theories. These theories are discussed in detail, in particular the gauge theories of quantum electrodynamics (QED) and of quantum chromodynamics (QCD), based on the gauge group SU(3). In both theories the gauge bosons, the photon and the gluons, have no mass. The gauge theory of the electroweak interactions, based on the gauge group SU(2) x U(1), describes both the electromagnetic and the weak interactions. The weak force is generated by the exchange of the weak bosons. They have a large mass, and one believes that these masses are generated by a spontaneous breaking of the gauge symmetry.It might be that the strong and the electroweak interactions are unified at very high energies ('Grand Unification'). The gauge groups SU(3) and SU(2) x U(1) must be subgroups of a big gauge group, describing the Grand Unification. Two such theories are discussed, based on the gauge groups SU(5) and SO(10).