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Ray, wave and quantum concepts are central to diverse and seemingly incompatible models of light. Each model particularizes a specific ''manifestation'' of light, and then corresponds to adequate physical assumptions and formal approximations, whose domains of applicability are well-established. Accordingly each model comprises its own set of geometric and dynamic postulates with the pertinent mathematical means.At a basic level, the book is a complete introduction to the Wigner optics, which bridges between ray and wave optics, offering the optical phase space as the ambience and the

Wave theory of light. --- Wigner distribution. --- Geometrical optics --- Mathematics. --- Optics, Geometrical --- Optics --- Distribution (Probability theory) --- Racah algebra --- Light, Wave theory of --- Wave-motion, Theory of --- Wave-particle duality

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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.

Electromagnetic theory. --- Wave theory of light. --- Vacuum. --- Quantum electrodynamics. --- Electrodynamics, Quantum --- QED (Physics) --- Quantum field theory --- Schwinger action principle --- High vacuum technique --- Electric discharges through gases --- Light, Wave theory of --- Optics --- Wave-motion, Theory of --- Wave-particle duality --- Light, Electromagnetic theory of --- Electric fields --- Magnetic fields

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Classical asymptotic expansions, while producing a good approximation for the diffracted fields in general, appear hardly applicable in the case of extremely elongated bodies. Thus, there are problems that are on the one hand too difficult for numerical solvers due to large system size, and on the other hand make the description with classical asymptotic methods hard. The book explains why this happens and suggests the way out. By defining the characteristics of a strongly elongated body it introduces a special class of asymptotic approximations, which are in some sense uniform with respect to the rate of body elongation. Chapter 1 briefly describes the results of V. A. Fock and further developments of his approach towards the problems of diffraction by elongated obstacles. It formulates the cases of moderately and strongly elongated bodies. The rest of the book describes the approach of special parabolic equations, which lead to new asymptotic approximations for the diffracted fields. Chapters 2, 3 and 4 discuss diffraction by bodies of elliptical shape: The elliptic cylinder with a strongly elongated cross section and prolate spheroid with a high aspect ratio. Chapter 5 generalizes the approach to some other shapes such as narrow cones and narrow hyperboloids. Mathematical formulas for the Whittaker functions widely used in the book are collected in the Appendix. The concise derivations are supplied with numerous test examples that compare asymptotic approximations with numerically computed fields and clarify the specifics of high frequency diffraction by strongly elongated bodies. The reference solutions presented in the book enable one to validate the newly developed numerical solvers.

Geometrical optics. --- Wave theory of light. --- Electrodynamics. --- Mathematical physics. --- Acoustics. --- Classical Optics, Geometric and Wave optics. --- Classical Electrodynamics. --- Mathematical Methods in Physics. --- Physical mathematics --- Physics --- Mathematics --- Dynamics --- Light, Wave theory of --- Optics --- Wave-motion, Theory of --- Wave-particle duality --- Optics, Geometrical --- Diffraction. --- Light

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Quantum mechanics, discovered by Werner Heisenberg and Erwin Schrödinger in 1925-1926, is famous for its radical implications for our conception of physics and for our view of human knowledge in general. While these implications have been seen as scientifically productive and intellectually liberating to some, Niels Bohr and Heisenberg, among them, they have been troublesome to many others, including Schrödinger and, most famously, Albert Einstein. The situation led to the intense debate that started in the wake of its discovery and has continued into our own time, with no end appearing to be in sight. Epistemology and Probability aims to contribute to our understanding of quantum mechanics and of the reasons for its extraordinary impact by reconsidering, under the rubric of "nonclassical epistemology," the nature of epistemology and probability, and their relationships in quantum theory. The book brings together the thought of the three figures most responsible for the rise of quantum mechanics—Heisenberg and Schrödinger, on the physical side, and Bohr, on the philosophical side—in order to develop a deeper sense of the physical, mathematical, and philosophical workings of quantum-theoretical thinking. Reciprocally, giving a special emphasis on probability and specifically to the Bayesian concept of probability allows the book to gain new insights into the thought of these figures. The book reconsiders, from this perspective, the Bohr-Einstein debate on the epistemology of quantum physics and, in particular, offers a new treatment of the famous experiment of Einstein, Podolsky, and Rosen (EPR), and of the Bohr-Einstein exchange concerning the subject. It also addresses the relevant aspects of quantum information theory and considers the implications of its epistemological argument for higher-level quantum theories, such as quantum field theory and string and brane theories. One of the main contributions of the book is its analysis of the role of mathematics in quantum theory and in the thinking of Bohr, Heisenberg, and Schrödinger, in particular an examination of the new (vis-à-vis classical physics and relativity) type of the relationships between mathematics and physics introduced by Heisenberg in the course of his discovery of quantum mechanics. Although Epistemology and Probability is aimed at physicists, philosophers and historians of science, and graduate and advanced undergraduate students in these fields, it is also written with a broader audience in mind and is accessible to readers unfamiliar with the higher-level mathematics used in quantum theory.

Schro ̈dinger equation. --- Schro ̈dinger, Erwin,. --- Quantum theory --- Physics --- Knowledge, Theory of --- Complementarity (Physics) --- Wave-particle duality --- Causality (Physics) --- Heisenberg uncertainty principle --- Schrèodinger equation --- Physical Sciences & Mathematics --- Atomic Physics --- History --- Mathematics --- Philosophy --- Knowledge, Theory of. --- Wave-particle duality. --- Heisenberg uncertainty principle. --- Schrd̲inger equation. --- History. --- Mathematics. --- Philosophy. --- Bohr, Niels, --- Schrödinger, Erwin, --- Heisenberg, Werner, --- Indeterminancy principle --- Uncertainty principle --- Causality --- Dualism, Wave-particle --- Duality principle (Physics) --- Wave-corpuscle duality --- Epistemology --- Theory of knowledge --- Geĭzenberg, V. --- Heisenberg, W. --- Heisenberg, Werner --- Schredinger, Ervin, --- Schrödinger, E. --- Boer, Niersi, --- Boerh, Niersi, --- Bohr, N. --- Bohr, Niels Henrik David, --- Bor, Nil's, --- Physics. --- Epistemology. --- Philosophy and science. --- Probabilities. --- Quantum physics. --- Elementary particles (Physics). --- Quantum field theory. --- Elementary Particles, Quantum Field Theory. --- Probability Theory and Stochastic Processes. --- Quantum Physics. --- Philosophy of Science. --- Nuclear physics --- Electromagnetic waves --- Matter --- Radiation --- Wave mechanics --- Psychology --- Constitution --- Schroedinger, Erwin,

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This book serves as an introductory text for students and engineers with limited knowledge of metamaterials (and elastic waves). This text begins with the most straightforward vibrating systems, such as single and 2-DOF spring-mass systems. It examines the observed phenomena in 2-DOF systems in an unconventional manner to prepare the reader for research on metamaterials. After presenting wave phenomena in an infinitely connected spring-mass system, an elastic bar, a continuous version of an infinite system, is analyzed. This instructional strategy, which progresses from the discrete model to the continuous model, facilitates efficient comprehension of wave and metamaterial concepts. Using continuous and discrete one-dimensional models, bending waves and their manipulation through metamaterials are also discussed. In the latter chapters of this book, advanced readers are introduced to the fundamental wave phenomena in two-dimensional media and wave manipulation using metamaterials, such as mode-converting transmission. As wave phenomena are the fundamental phenomena in vibrating structures, those interested in acoustics and vibration would gain a great deal of knowledge from this book, as the material covered in it offers a very different perspective on oscillatory phenomena than what is typically found in books on acoustics and vibration. Because this book presents a new technique for manipulating waves using metamaterials, engineers and scientists who work with (ultra)sounds and structural vibrations would find it very useful for expanding their knowledge of relevant topics.

Plasma waves. --- Metamaterials. --- Telecommunication. --- Photonics. --- Geometrical optics. --- Wave theory of light. --- Waves, instabilities and nonlinear plasma dynamics. --- Microwaves, RF Engineering and Optical Communications. --- Ultrafast Photonics. --- Classical Optics, Geometric and Wave optics. --- Light, Wave theory of --- Optics --- Wave-motion, Theory of --- Wave-particle duality --- Optics, Geometrical --- New optics --- Electric communication --- Mass communication --- Telecom --- Telecommunication industry --- Telecommunications --- Communication --- Information theory --- Telecommuting --- Meta materials --- Composite materials --- Electromagnetism --- Plasma sound waves --- Acoustic surface waves --- Magnetohydrodynamics --- Plasma (Ionized gases) --- Waves --- Elastic waves.