Arising out of the need for Quantum Mechanics (QM) to be part of the common education of mathematics students, this book formulates the mathematical structure of QM in terms of the C*-algebra of observables, which is argued on the basis of the operational definition of measurements and the duality between states and observables.
This book provides a readable account of the foundations of QFT, in particular of the Euclidean formulation with emphasis on the interplay between physical requirements and mathematical structures. The general structures underlying the conventional local (renormalizable) formulation of gauge QFT are discussed also on the basis of simple models. The mechanism of confinement, non-trivial topology and ?-vacua, chiral symmetry breaking and solution of the U(1) problem are clarified through a careful analysis of the Schwinger model, which settles unclear or debated points.
This book is a collection of lecture notes discussing the basic features of the Quantum Mechanics of Infinite Systems such as collective phenomena, spontaneous symmetry breaking, etc. The mathematical precision has been reduced to a minimum in order to communicate the main ideas to a larger audience including those who are not mathematically meinded. It is aimed at helping students who have difficulty in finding accessible and compact expositions of the material in standard textbooks.
The intriguing mechanism of spontaneous symmetry breaking is a powerful innovative idea at the basis of most of the recent developments in theoretical physics, from statistical mechanics to many-body theory to elementary particles theory; for infinitely extended systems a symmetric Hamiltonian can account for non symmetric behaviours, giving rise to non symmetric realizations of a physical system. In the first part of this book, devoted to classical field theory, such a mechanism is explained in terms of the occurrence of disjoint sectors and their stability properties and of an improved version of the Noether theorem. For infinitely extended quantum systems, discussed in the second part, the mechanism is related to the occurrence of disjoint pure phases and characterized by a symmetry breaking order parameter, for which non perturbative criteria are discussed, following Wightman, and contrasted with the standard Goldstone perturbative strategy. The Goldstone theorem is discussed with a critical look at the hypotheses that emphasizes the crucial role of the dynamical delocalization induced by the interaction range. The Higgs mechanism in local gauges is explained in terms of the Gauss law constraint on the physical states. The mathematical details are kept to the minimum required to make the book accessible to students with basic knowledge of Hilbert space structures. Much of the material has not appeared in other textbooks.
Arising out of the need for Quantum Mechanics (QM) to be part of the common education of mathematics students, this book formulates the mathematical structure of QM in terms of the C*-algebra of observables, which is argued on the basis of the operational definition of measurements and the duality between states and observables.
This book presents the basic elements of Analytical Mechanics, starting from the physical motivations that favor it with respect to the Newtonian Mechanics in Cartesian coordinates. Rather than presenting Analytical Mechanics mainly as a formal development of Newtonian Mechanics, it highlights its effectiveness due to the following five important achievements: 1) the most economical description of time evolution in terms of the minimal set of coordinates, so that there are no constraint forces in their evolution equations; 2) the form invariance of the evolution equations, which automatically solves the problem of fictitious forces; 3) only one scalar function encodes the formulation of the dynamics, rather than the full set of vectors which describe the forces in Cartesian Newtonian Mechanics; 4) in the Hamiltonian formulation, the corresponding evolution equations are of first order in time and are fully governed by the Hamiltonian function (usually corresponding to the energy); 5) the emergence of the Hamiltonian canonical algebra and its effectiveness in simplifying the control of the dynamical problem (e.g. the constant of motions identified by the Poisson brackets with the Hamiltonian, the relation between symmetries and conservations laws, the use of canonical transformations to reduce the Hamiltonian to a simpler form etc.). The book also addresses a number of points usually not included in textbook presentations of Analytical Mechanics, such as 1) the characterization of the cases in which the Hamiltonian differs from the energy, 2) the characterization of the non-uniqueness of the Lagrangian and of the Hamiltonian and its relation to a "gauge" transformation, 3) the Hamiltonian formulation of the Noether theorem, with the possibility that the constant of motion corresponding to a continuous symmetry of the dynamics is not the canonical generator of the symmetry transformation but also involves the generator of a gauge transformation. In turn, the book's closing chapter is devoted to explaining the extraordinary analogy between the canonical structure of Classical and Quantum Mechanics. By correcting the Dirac proposal for such an explanation, it demonstrates that there is a common Poisson algebra shared by Classical and Quantum Mechanics, the differences between the two theories being reducible to the value of the central variable of that algebra.
This book is a collection of lecture notes discussing the basic features of the Quantum Mechanics of Infinite Systems such as collective phenomena, spontaneous symmetry breaking, etc. The mathematical precision has been reduced to a minimum in order to communicate the main ideas to a larger audience including those who are not mathematically meinded. It is aimed at helping students who have difficulty in finding accessible and compact expositions of the material in standard textbooks.
This book provides a readable account of the foundations of QFT, in particular of the Euclidean formulation with emphasis on the interplay between physical requirements and mathematical structures. The general structures underlying the conventional local (renormalizable) formulation of gauge QFT are discussed also on the basis of simple models. The mechanism of confinement, non-trivial topology and ?-vacua, chiral symmetry breaking and solution of the U(1) problem are clarified through a careful analysis of the Schwinger model, which settles unclear or debated points.
International Series in Natural Philosophy, Volume 30: Problems in Quantum Mechanics focuses on the processes, principles, reactions, and methodologies involved in quantum mechanics. The publication first elaborates on the mathematical formalism of quantum mechanics, simple quantum systems, and mean values and uncertainty relations. Discussions focus on mean values of dynamical variables, uncertainty relations, eigenfunctions and the energy spectrum, motion in a central field, matrix representation of vectors and operators, Hubert spaces, and operators in Hilbert space. The text then takes a look at mean values and uncertainty relations, semi-classical approximation, and pictures and representations. The book takes a look at orbital angular momentum and spin, systems of identical particles, and perturbation theory. Topics include variational method, stationary state perturbation theory, isotopic spin, second quantization, properties of angular momentum operators, and angular momentum and rotations of coordinate axes. The manuscript also ponders on functions used in quantum mechanics, relativistic quantum mechanics, and radiation theory. The publication is a dependable reference for researchers interested in quantum mechanics.
This unique textbook examines the basic health and environmental issues associated with air pollution including the relevant toxicology and epidemiology. It provides a foundation for the sampling and analysis of air pollutants as well as an understanding of international air quality regulations. Written for upper-level undergraduate and introductory graduate courses in air pollution, the book is also a valuable desk reference for practicing professionals who need to have a broad understanding of the topic. Key features: - Provides the most up-to-date coverage of the basic health and environmental issues associated with air pollution. - Offers a broader examination of air pollution topics, beyond just the meteorological and engineering aspects of air pollution. - Includes the following Instructor Resources: Instructor's Manual, PowerPoint Presentations, and a TestBank. The Phalens have put together a timely book on a critically important topic that affects all of us -- air pollution - and they do so in a new and highly relevant way: they consider the broad societal health impacts from a fundamental science viewpoint. The epidemiology, toxicology, and risks of air pollutants are included, and ethical issues of concern are highlighted. This book is a must-read for students who wish to become professionals in the air quality field and for students of environmental science whose work includes air pollution issues. The book is a significant contribution to the discipline." - Cliff I. Davidson, Director, Center for Sustainable Engineering; Thomas C. and Colleen L. Wilmot Professor of Engineering, Syracuse Center of Excellence in Environmental and Energy Systems and Department of Civil and Environmental Engineering, Syracuse University "Truly, human well-being and public health in the 21st century may hinge on our ability to anticipate, recognize, evaluate, control, and confirm responsible management of air pollution. This timely, informative, and insightful text provides a solid introduction for students and a technically sound handbook for professionals seeking literacy and critical thinking, real-life examples, understanding (not just rote applications), opportunities for continuous improvement, and modern tools for assessing and managing current and evolving air pollution challenges." - Mark D. Hoover, PhD, CHP, CIH Aerosol and health science researcher, author, and editor
With the 13th edition, Wintrobe’s Clinical Hematology once again bridges the gap between the clinical practice of hematology and the basic foundations of science. Broken down into eight parts, this book provides readers with a comprehensive overview of: Laboratory Hematology, The Normal Hematologic System, Transfusion Medicine, Disorders of Red Cells, Hemostasis and Coagulation; Benign Disorders of Leukocytes, The Spleen and/or Immunoglobulins; Hematologic Malignancies, and Transplantation. Within these sections, there is a heavy focus on the morphological exam of the peripheral blood smear, bone marrow, lymph nodes, and other tissues. With the knowledge about gene therapy and immunotherapy expanding, new, up-to-date information about the process and application of these therapies is included. Likewise, the editors have completely revised material on stem cell transplantation in regards to both malignant and benign disorders, graft versus host disease, and the importance of long-term follow-up of transplantation survivors.
Since the discovery of the corpuscular nature of radiation by Planck more than fifty years ago the quantum theory of radiation has gone through many stages of development which seemed to alternate between spectacular success and hopeless frustration. The most recent phase started in 1947 with the discovery of the electromagnetic level shifts and the realization that the exist ing theory, when properly interpreted, was perfectly adequate to explain these effects to an apparently unlimited degree of accuracy. This phase has now reached a certain conclusion: for the first time in the checkered history of this field of research it has become possible to give a unified and consistent presen tation of radiation theory in full conformity with the principles of relativity and quantum mechanics. To this task the present book is devoted. The plan for a book of this type was conceived during the year 1951 while the first-named author (J. M. J. ) held a Fulbright research scholarship at Cambridge University. During this year of freedom from teaching and other duties he had the opportunity of conferring with physicists in many different countries on the recent developments in radiation theory. The comments seemed to be almost unanimous that a book on quantum electrodynamics at the present time would be of inestimable value to physicists in many parts of the world. However, it was not until the spring of 1952 that work on the book began in earnest.
This book describes, by using elementary techniques, how some geometrical structures widely used today in many areas of physics, like symplectic, Poisson, Lagrangian, Hermitian, etc., emerge from dynamics. It is assumed that what can be accessed in actual experiences when studying a given system is just its dynamical behavior that is described by using a family of variables ("observables" of the system). The book departs from the principle that ''dynamics is first'' and then tries to answer in what sense the sole dynamics determines the geometrical structures that have proved so useful to describe the dynamics in so many important instances. In this vein it is shown that most of the geometrical structures that are used in the standard presentations of classical dynamics (Jacobi, Poisson, symplectic, Hamiltonian, Lagrangian) are determined, though in general not uniquely, by the dynamics alone. The same program is accomplished for the geometrical structures relevant to describe quantum dynamics. Finally, it is shown that further properties that allow the explicit description of the dynamics of certain dynamical systems, like integrability and super integrability, are deeply related to the previous development and will be covered in the last part of the book. The mathematical framework used to present the previous program is kept to an elementary level throughout the text, indicating where more advanced notions will be needed to proceed further. A family of relevant examples is discussed at length and the necessary ideas from geometry are elaborated along the text. However no effort is made to present an ''all-inclusive'' introduction to differential geometry as many other books already exist on the market doing exactly that. However, the development of the previous program, considered as the posing and solution of a generalized inverse problem for geometry, leads to new ways of thinking and relating some of the most conspicuous geometrical structures appearing in Mathematical and Theoretical Physics.
Analytical Chemistry, Volume 38: Ion Exchange in Analytical Chemistry provides a broad survey of the important role that ion exchange can and should play in chemical analysis. This book focuses on the plate-equilibrium theory of chromatography, which is less difficult theoretically than the mass-transfer theory. Organized into 11 chapters, this volume begins with an overview of the earliest recorded application of ion exchange. This text then examines how high temperature affects ion-exchange resins. Other chapters consider the exchange of ions between a solid ion-exchanging material and a solution, which is a typically reversible reaction. This book describes as well the relatively simple separations and other applications of ion exchange to analytical chemistry. The final chapter deals with the interesting nature of the metal complexes formed within the exchanger and describe the use of ion-exchange distribution studies to determine the stability and nature of complexes existing in the solution. This book is a valuable resource for analytical chemists.
Morson and Dawson's Gastrointestinal Pathology is one of the 'Gold Standards' of pathology textbooks. It has been completely revised to incorporate the latest advances in this rapidly evolving field including the developments in gastric cancer and Helicobacter pylori and the revised classification of other common gastrointestinal conditions. This new edition features a wealth of new material presented in full colour for the first time.
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