Mathematics is an essential ingredient in the education of a student of mathematics or physics of a professional physicist, indeed in the education of any professional scientist or engineer. The purpose of Mathematical Physics is to provide a comprehensive study of the mathematics underlying theoretical physics at the level of graduate and postgraduate students and also have enough depth for others interested in higher level mathematics relevant to specialized fields. It is also intended to serve the research scientist or engineer who needs a quick refresher course in the subject. The Fourth Edition of the book has been thoroughly revised and updated keeping in mind the requirements of students and the latest UGC syllabus.
This invaluable book is an introduction to knot and link invariants as generalized amplitudes for a quasi-physical process. The demands of knot theory, coupled with a quantum-statistical framework, create a context that naturally and powerfully includes an extraordinary range of interrelated topics in topology and mathematical physics. The author takes a primarily combinatorial stance toward knot theory and its relations with these subjects. This stance has the advantage of providing direct access to the algebra and to the combinatorial topology, as well as physical ideas. The book is divided into two parts: Part I is a systematic course on knots and physics starting from the ground up, and Part II is a set of lectures on various topics related to Part I. Part II includes topics such as frictional properties of knots, relations with combinatorics, and knots in dynamical systems. In this new edition, an article on Virtual Knot Theory and Khovanov Homology has beed added. Contents:Physical KnotsStates and the Bracket PolynomialThe Jones Polynomial and Its GeneralizationsBraids and the Jones PolynomialFormal Feynman Diagrams, Bracket as a Vacuum-Vacuum Expectation and the Quantum Group SL(2)qYang–Baxter Models for Specializations of the Homfly PolynomialKnot-Crystals — Classical Knot Theory in a Modern GuiseThe Kauffman PolynomialThree Manifold Invariants from the Jones PolynomialIntegral Heuristics and Witten's InvariantsThe Chromatic PolynomialThe Potts Model and the Dichromatic PolynomialThe Penrose Theory of Spin NetworksKnots and Strings — Knotted StringsDNA and Quantum Field TheoryKnots in Dynamical Systems — The Lorenz Attractorand selected papers Readership: Physicists and mathematicians. Keywords:Knots;Kauffman;Jones PolynomialReviews: "This book is an essential volume for the student of low-dimensional topology from which a serious student can learn most aspects of modern knot theory. Its informal tone encourages investigation on the part of the reader. The author leaves the reader items to puzzle out." Mathematical Reviews Reviews of the Third Edition: “It is an attractive book for physicists with profuse and often entertaining illustrations … proofs … seldom heavy and nearly always well explained with pictures … succeeds in infusing his own excitement and enthusiasm for these discoveries and their potential implications.” Physics Today “The exposition is clear and well illustrated with many examples. The book can be recommended to everyone interested in the connections between physics and topology of knots.” Mathematics Abstracts “… here is a gold mine where, with care and patience, one should get acquainted with a beautiful subject under the guidance of a most original and imaginative mind.” Mathematical Reviews
'The book in your hands develops the best traditions of the Russian scientific popular literature. Written in a clear and captivating manner by working theoretical physicists, who are, at the same time, dedicated popularizers of scientific knowledge, it brings to the reader the latest achievements in quantum solid-state physics, but along the way it also shows how the laws of physics reveal themselves even in seemingly trivial episodes concerning the natural phenomena around us. And most importantly, it shows that we live in the world, where scientists are capable of 'proving harmony with algebra.' — A A Abrikosov, 2003 Nobel Prize Winner in Physics
A dynamic, all-inclusive overview of the field of health physics If it's an important topic in the field of health physics, you'll find it in this trusted text . . . in sections on physical principles, atomic and nuclear structure, radioactivity, biological effects of radiation, and instrumentation. This one-of-a-kind guide spans the entire scope of the field and offers a problem-solving approach that will serve you throughout your career. Features: A thorough overview of need-to-know topics, from a review of physical principles to a useful look at the interaction of radiation with matter Chapter-ending practice problems to solidify your grasp of health physics topics and their real-world application Essential background material on quantitative risk assessment for health-threatening radiation dangers Authoritative radiation safety and environmental health coverage that supports the International Commission on Radiological Protection's standards for specific populations High-yield appendices to expand your comprehension of chapter material: Values of Some Useful Constants, Table of the Elements, The Reference Person, Specific Absorbed Fraction of Photon Energy, and Total Mass Attenuation Coefficients NEW! Essential coverage of non-ionizing radiation-laser and microwaves, computer use in dose calculation, and dose limit recommendations
This course study guide is to be used with New Understanding Physics for Advanced Level or other physics core textbooks. It aims to help further develop physics skills such as laboratory techniques, mathematical methods and data handling. The course study guide also provides outline solutions to a selection of questions and gives advice on answering all types of examination questions and support for Key Skills.