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.
Biophotonic diagnostics/biomedical spectroscopy can revolutionise the medical environment by providing a responsive and objective diagnostic environment. This book aims to explain the fundamentals of the physical techniques used combined with the particular requirements of analysing medical/clinical samples as a resource for any interested party. In addition, it will show the potential of this field for the future of medical science and act as a driver for translation across many different biological problems/questions.
Jet physics is an incredibly rich subject detailing the narrow cone of hadrons and other particles produced by the hadronization of a quark or gluon in a particle physics or heavy ion experiment. This book is a general overview of jet physics for scientists not directly involved in the field. It presents the basic experimental and theoretical problems arising when dealing with jets, and describing the solutions proposed in recent years.
This book provides a general description of the search for and discovery of the Higgs boson (particle) at CERN’s Large Hadron Collider. The goal is to provide a relatively brief overview of the issues, instruments and techniques relevant for this search; written by a physicist who was directly involved. The Higgs boson mat be the one particle that was studied the most before its discovery and the story from postulation in 1964 to detection in 2012 is a fascinating one. The story is told here while detailing the fundamentals of particle physics.
Order from chaos is simultaneously a mantra of physics and a reality in biology. Physicist Norman Packard suggested that life developed and thrives at the edge of chaos. Questions remain, however, as to how much practical knowledge of biology can be traced to existing physical principles, and how much physics has to change in order to address the complexity of biology. Phil Anderson, a physics Nobel laureate, contributed to popularizing a new notion of the end of “reductionism.” In this view, it is necessary to abandon the quest of reducing complex behavior to known physical results, and to identify emergent behaviors and principles. In the present book, however, we have sought physical rules that can underlie the behavior of biota as well as the geochemistry of soil development. We looked for fundamental principles, such as the dominance of water flow paths with the least cumulative resistance, that could maintain their relevance across a wide range of spatial and temporal scales, together with the appropriate description of solute transport associated with such flow paths. Thus, ultimately, we address both nutrient and water transport limitations of processes from chemical weathering to vascular plant growth. The physical principles guiding our effort are established in different, but related concepts and fields of research, so that in fact our book applies reductionist techniques guided by analogy. The fact that fundamental traits extend across biotic and abiotic processes, i.e., the same fluid flow rate is relevant to both, but that distinctions in topology of the connected paths lead to dramatic differences in growth rates, helps unite the study of these nominally different disciplines of geochemistry and geobiology within the same framework. It has been our goal in writing this book to share the excitement of learning, and one of the most exciting portions to us has been the ability to bring some order to the question of the extent to which soils can facilitate plant growth, and what limitations on plant sizes, metabolism, occurrence, and correlations can be formulated thereby. While we bring order to the soil constraints on growth , we also generate some uncertainties in the scaling relationships of plant growth and metabolism. Although we have made an first attempt to incorporate edaphic constraints into allometric scaling, this is but an initial foray into the forest.
Quantum information is an emerging field which has attracted a lot of attention in the last couple of decades. It is a broad subject which extends from the most applied questions (e.g. how to build quantum computers or secure cryptographic systems) to the most theoretical problems concerning the formalism and interpretation of quantum mechanics, its complexity, and its potential to go beyond classical physics. This book is an introduction to quantum information with special emphasis on continuous-variable systems (such as light) which can be described as collections of harmonic oscillators. It covers a selection of basic concepts, focusing on their physical meaning and mathematical treatment. It starts from the very first principles of quantum mechanics, and builds up the concepts and techniques following a logical progression. This is an excellent reference for students with a full semester of standard quantum mechanics and researchers in closely related fields.
This volume is a basic introduction to certain aspects of elliptic functions and elliptic integrals. Primarily, the elliptic functions stand out as closed solutions to a class of physical and geometrical problems giving rise to nonlinear differential equations. While these nonlinear equations may not be the types of greatest interest currently, the fact that they are solvable exactly in terms of functions about which much is known makes up for this. The elliptic functions of Jacobi, or equivalently the Weierstrass elliptic functions, inhabit the literature on current problems in condensed matter and statistical physics, on solitons and conformal representations, and all sorts of famous problems in classical mechanics. The lectures on elliptic functions have evolved as part of the first semester of a course on theoretical and mathematical methods given to first and second year graduate students in physics and chemistry at the University of North Dakota. They are for graduate students or for researchers who want an elementary introduction to the subject that nevertheless leaves them with enough of the details to address real problems. The style is supposed to be informal. The intention is to introduce the subject as a moderate extension of ordinary trigonometry in which the reference circle is replaced by an ellipse. This entre depends upon fewer tools and has seemed less intimidating that other typical introductions to the subject that depend on some knowledge of complex variables. The first three lectures assume only calculus, including the chain rule and elementary knowledge of differential equations. In the later lectures, the complex analytic properties are introduced naturally so that a more complete study becomes possible.
The present theme concerns the forces of nature, and what investigations of these forces can tell us about the world we see about us. The story of these forces is long and complex, and contains many episodes that are not atypical of the bulk of scientific research, which could have achieved greater acclaim 'if only…'. The intention of this book is to introduce ideas of how the visible world, and those parts of it that we cannot observe, either because they are too small or too large for our scale of perception, can be understood by consideration of only a few fundamental forces. The subject in these pages will be the authority of the commonly termed, laws of physics, which arise from the forces of nature, and the corresponding constants of nature (for example, the speed of light, c, the charge of the electron, e, or the mass of the electron, me).
Cosmology is the study of the origin, size, and evolution of the entire universe. Every culture has developed a cosmology, whether it be based on religious, philosophical, or scientific principles. In this book, the evolution of the scientific understanding of the Universe in Western tradition is traced from the early Greek philosophers to the most modern 21st century view. After a brief introduction to the concept of the scientific method, the first part of the book describes the way in which detailed observations of the Universe, first with the naked eye and later with increasingly complex modern instruments, ultimately led to the development of the «Big Bang» theory. The second part of the book traces the evolution of the Big Bang including the very recent observation that the expansion of the Universe is itself accelerating with time.
Structure and Evolution of Single Stars: An introduction is intended for upper-level undergraduates and beginning graduates with a background in physics. Following a brief overview of the background observational material, the basic equations describing the structure and evolution of single stars are derived. The relevant physical processes, which include the equation of state, opacity, nuclear reactions and neutrino losses are then reviewed. Subsequent chapters describe the evolution of low-mass stars from formation to the final white dwarf phase. The final chapter deals with the evolution of massive stars.