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Physics of the Lorentz Group
This book explains the Lorentz mathematical group in a language familiar to physicists. While the three-dimensional rotation group is one of the standard mathematical tools in physics, the Lorentz group of the four-dimensional Minkowski space is still very strange to most present-day physicists. It plays an essential role in understanding particles moving at close to light speed and is becoming the essential language for quantum optics, classical optics, and information science. The book is based on papers and books published by the authors on the representations of the Lorentz group based on harmonic oscillators and their applications to high-energy physics and to Wigner functions applicable to quantum optics. It also covers the two-by-two representations of the Lorentz group applicable to ray optics, including cavity, multilayer and lens optics, as well as representations of the Lorentz group applicable to Stokes parameters and the Poincaré sphere on polarization optics.
Harmonic Oscillators and Two-By-Two Matrices in Symmetry Problems in Physics
This book is a printed edition of the Special Issue "Harmonic Oscillators In Modern Physics" that was published in Symmetry
Mathematical Devices for Optical Sciences
The Lorentz group, which is the underlying scientific language for modern optics, has most notably been used for understanding Einstein's special relativity. By using a simplified approach of two-by-two matrices and Wigner functions, this book provides a basic and novel approach to classical and quantum optics, making these difficult subjects more transparent to the reader. Written by three experts in the field, Sibel Başkal, Young S Kim and Marilyn E Noz, this book will provide the reader with a comprehensive overview of how fundamental issues in quantum mechanics can be approached using various optical instruments, Wigner functions and quantum entanglement.
Selected Papers from the 16th International Conference on Squeezed States and Uncertainty Relations (ICSSUR 2019)
The first quantum revolution started in the early 20th century and gave us new rules that govern physical reality. Accordingly, many devices that changed dramatically our lifestyle, such as transistors, medical scanners and lasers, appeared in the market. This was the origin of quantum technology, which allows us to organize and control the components of a complex system governed by the laws of quantum physics. This is in sharp contrast to conventional technology, which can only be understood within the framework of classical mechanics. We are now in the middle of a second quantum revolution. Although quantum mechanics is nowadays a mature discipline, quantum engineering as a technology is n...
Physics of Lorentz Group Second Editiohb
This book explains the Lorentz group in a language familiar to physicists, namely in terms of two-by-two matrices. While the three-dimensional rotation group is one of the standard mathematical tools in physics, the Lorentz group applicable to the four-dimensional Minkowski space is still very strange to most physicists. However, it plays an essential role in a wide swathe of physics and is becoming the essential language for modern and rapidly developing fields. The first edition was primarily based on applications in high-energy physics developed during the latter half of the 20th Century, and the application of the same set of mathematical tools to optical sciences. In this new edition, t...
Mathematical Devices for Optical Sciences
"The Lorentz group which is the underlying scientific language for modern optics has been most notably used for understanding Einstein's special relativity. By using a simplified approach of two-by-two matrices and Wigner functions, this book provides a basic and novel approach to classical and quantum optics, making these often-difficult subjects more transparent to the reader. Written by three experts in the field, Professors Sibel Baðskal, Young S. Kim, and Marilyn E Noz, this book will give the reader a comprehensive overview of how fundamental issues in quantum mechanics can be approached using various optical instruments, Wigner functions, and quantum entanglement." -- Prové de l'editor.
Theory and Applications of the Poincaré Group
Special relativity and quantum mechanics, formulated early in the twentieth century, are the two most important scientific languages and are likely to remain so for many years to come. In the 1920's, when quantum mechanics was developed, the most pressing theoretical problem was how to make it consistent with special relativity. In the 1980's, this is still the most pressing problem. The only difference is that the situation is more urgent now than before, because of the significant quantity of experimental data which need to be explained in terms of both quantum mechanics and special relativity. In unifying the concepts and algorithms of quantum mechanics and special relativity, it is impor...
Phase Space Picture of Quantum Mechanics
This book covers the theory and applications of the Wigner phase space distribution function and its symmetry properties. The book explains why the phase space picture of quantum mechanics is needed, in addition to the conventional Schrödinger or Heisenberg picture. It is shown that the uncertainty relation can be represented more accurately in this picture. In addition, the phase space picture is shown to be the natural representation of quantum mechanics for modern optics and relativistic quantum mechanics of extended objects. Contents:Phase Space in Classical MechanicsForms of Quantum MechanicsWigner Phase- Space Distribution FunctionsLinear Canonical Transformations in Quantum Mechanics...
Dynamical Symmetry
Whenever systems are governed by continuous chains of causes and effects, their behavior exhibits the consequences of dynamical symmetries, many of them far from obvious. Dynamical Symmetry introduces the reader to Sophus Lie's discoveries of the connections between differential equations and continuous groups that underlie this observation. It develops and applies the mathematical relations between dynamics and geometry that result. Systematic methods for uncovering dynamical symmetries are described, and put to use. Much material in the book is new and some has only recently appeared in research journals. Though Lie groups play a key role in elementary particle physics, their connection with differential equations is more often exploited in applied mathematics and engineering. Dynamical Symmetry bridges this gap in a novel manner designed to help readers establish new connections in their own areas of interest. Emphasis is placed on applications to physics and chemistry. Applications to many of the other sciences illustrate both general principles and the ubiquitousness of dynamical symmetries.
Mathematical Optics
Going beyond standard introductory texts, Mathematical Optics: Classical, Quantum, and Computational Methods brings together many new mathematical techniques from optical science and engineering research. Profusely illustrated, the book makes the material accessible to students and newcomers to the field. Divided into six parts, the text presents state-of-the-art mathematical methods and applications in classical optics, quantum optics, and image processing. Part I describes the use of phase space concepts to characterize optical beams and the application of dynamic programming in optical waveguides. Part II explores solutions to paraxial, linear, and nonlinear wave equations. Part III discu...
