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Author: Kai S Lam Publisher: World Scientific Publishing Company ISBN: 981466782X Category : Science Languages : en Pages : 851
Book Description
This new (second) edition contains a general treatment of quantum field theory (QFT) in a simple scalar field setting in addition to the modern material on the applications of differential geometry and topology, group theory, and the theory of linear operators to physics found in the first edition. All these are introduced without assuming more background on the part of the reader than a good foundation in undergraduate (junior) level mathematical physics. The new material entirely focuses on an introduction to quantum field theory, emphasizing the Feynman path (functional integral) approach to QFT and the renormalization group. With respect to the latter, the focus is on an introduction of its application to critical phenomena in statistical physics, following the outgrowth of the Callan-Symanzik equation originally developed in the context of high energy physics, and the seminal contributions of Kenneth Wilson. One of the overriding aims of the new material is also to draw students' attention to the deep connections between high energy physics and statistical mechanics. The unavoidable technical aspects are explained with a minimum of prerequisite material and jargon, and conceptual understanding is always given prominence before mastery of technical details, but the importance of the latter is never underestimated. Derivational details and motivational discussions are provided in abundance in order to ensure continuity of reading, and to avoid trying the readers' patience.
Author: Kai S Lam Publisher: World Scientific Publishing Company ISBN: 981466782X Category : Science Languages : en Pages : 851
Book Description
This new (second) edition contains a general treatment of quantum field theory (QFT) in a simple scalar field setting in addition to the modern material on the applications of differential geometry and topology, group theory, and the theory of linear operators to physics found in the first edition. All these are introduced without assuming more background on the part of the reader than a good foundation in undergraduate (junior) level mathematical physics. The new material entirely focuses on an introduction to quantum field theory, emphasizing the Feynman path (functional integral) approach to QFT and the renormalization group. With respect to the latter, the focus is on an introduction of its application to critical phenomena in statistical physics, following the outgrowth of the Callan-Symanzik equation originally developed in the context of high energy physics, and the seminal contributions of Kenneth Wilson. One of the overriding aims of the new material is also to draw students' attention to the deep connections between high energy physics and statistical mechanics. The unavoidable technical aspects are explained with a minimum of prerequisite material and jargon, and conceptual understanding is always given prominence before mastery of technical details, but the importance of the latter is never underestimated. Derivational details and motivational discussions are provided in abundance in order to ensure continuity of reading, and to avoid trying the readers' patience.
Author: Kai S. Lam Publisher: World Scientific ISBN: 9789812384546 Category : Science Languages : en Pages : 622
Book Description
This textbook, pitched at the advanced-undergraduate to beginning-graduate level, focuses on mathematical topics of relevance in contemporary physics that are not usually covered in texts at the same level. Its main purpose is to help students appreciate and take advantage of the modern trend of very productive symbiosis between physics and mathematics. Three major areas are covered: (1) linear operators; (2) group representations and Lie algebra representations; (3) topology and differential geometry.The following are noteworthy features of this book: the style of exposition is a fusion of those common in the standard physics and mathematics literatures; the level of exposition varies from quite elementary to moderately advanced, so that the book is of interest to a wide audience; despite the diversity of the topics covered, there is a strong degree of thematic unity; much care is devoted to detailed cross-referencing so that, from any part of the book, the reader can trace easily where specific concepts or techniques are introduced.
Author: Kai S Lam Publisher: World Scientific Publishing Company ISBN: 9813102306 Category : Science Languages : en Pages : 620
Book Description
This textbook, pitched at the advanced-undergraduate to beginning-graduate level, focuses on mathematical topics of relevance in contemporary physics that are not usually covered in texts at the same level. Its main purpose is to help students appreciate and take advantage of the modern trend of very productive symbiosis between physics and mathematics. Three major areas are covered: (1) linear operators; (2) group representations and Lie algebra representations; (3) topology and differential geometry.The following are noteworthy features of this book: the style of exposition is a fusion of those common in the standard physics and mathematics literatures; the level of exposition varies from quite elementary to moderately advanced, so that the book is of interest to a wide audience; despite the diversity of the topics covered, there is a strong degree of thematic unity; much care is devoted to detailed cross-referencing so that, from any part of the book, the reader can trace easily where specific concepts or techniques are introduced.
Author: Kai Shue Lam Publisher: World Scientific ISBN: 9789812384041 Category : Science Languages : en Pages : 628
Book Description
This textbook, pitched at the advanced-undergraduate to beginning-graduate level, focuses on mathematical topics of relevance in contemporary physics that are not usually covered in texts at the same level. Its main purpose is to help students appreciate and take advantage of the modern trend of very productive symbiosis between physics and mathematics. Three major areas are covered: (1) linear operators; (2) group representations and Lie algebra representations; and (3) topology and differential geometry. The features of this work include: an exposition style which is a fusion of those common in the standard physics and mathematics literatures; a level of exposition that varies from quite elementary to moderately advanced, so that the text should be of interest to a wide audience; a strong degree of thematic unity, despite the diversity of the topics covered; and cross references, so that, from any part of the book, the reader can trace easily where specific concepts or techniques are introduced.
Author: Roman W. Jackiw Publisher: World Scientific ISBN: 9789810216979 Category : Science Languages : en Pages : 528
Book Description
In this volume, topics are drawn from field theory, especially gauge field theory, as applied to particle, condensed matter and gravitational physics, and concern a variety of interesting subjects. These include geometricalDtopological effects in quantum theory, fractional charge, time travel, relativistic quantized fields in and out of thermal equilibrium and quantum modifications of symmetry in physical systems.Many readers will find this a useful volume, especially theoretical physicists and mathematicians. The material will be of interest to both the expert who will find well-presented novel and stimulating viewpoints of various subjects and the novice who will find complete, detailed and precise descriptions of important topics of current interest, in theoretical and mathematical physics.
Author: Kouei Sekigawa Publisher: World Scientific ISBN: 9814475025 Category : Mathematics Languages : en Pages : 350
Book Description
This volume contains the contributions by the participants in the eight of a series workshops in complex analysis, differential geometry and mathematical physics and related areas.Active specialists in mathematical physics contribute to the volume, providing not only significant information for researchers in the area but also interesting mathematics for non-specialists and a broader audience. The contributions treat topics including differential geometry, partial differential equations, integrable systems and mathematical physics.
Author: Don Koks Publisher: Springer Science & Business Media ISBN: 0387309438 Category : Science Languages : en Pages : 549
Book Description
Have you ever wondered why the language of modern physics centres on geometry? Or how quantum operators and Dirac brackets work? What a convolution really is? What tensors are all about? Or what field theory and lagrangians are, and why gravity is described as curvature? This book takes you on a tour of the main ideas forming the language of modern mathematical physics. Here you will meet novel approaches to concepts such as determinants and geometry, wave function evolution, statistics, signal processing, and three-dimensional rotations. You will see how the accelerated frames of special relativity tell us about gravity. On the journey, you will discover how tensor notation relates to vector calculus, how differential geometry is built on intuitive concepts, and how variational calculus leads to field theory. You will meet quantum measurement theory, along with Green functions and the art of complex integration, and finally general relativity and cosmology. The book takes a fresh approach to tensor analysis built solely on the metric and vectors, with no need for one-forms. This gives a much more geometrical and intuitive insight into vector and tensor calculus, together with general relativity, than do traditional, more abstract methods. Don Koks is a physicist at the Defence Science and Technology Organisation in Adelaide, Australia. His doctorate in quantum cosmology was obtained from the Department of Physics and Mathematical Physics at Adelaide University. Prior work at the University of Auckland specialised in applied accelerator physics, along with pure and applied mathematics.
Author: Robert Geroch Publisher: University of Chicago Press ISBN: 022622306X Category : Science Languages : en Pages : 358
Book Description
Mathematical Physics is an introduction to such basic mathematical structures as groups, vector spaces, topological spaces, measure spaces, and Hilbert space. Geroch uses category theory to emphasize both the interrelationships among different structures and the unity of mathematics. Perhaps the most valuable feature of the book is the illuminating intuitive discussion of the "whys" of proofs and of axioms and definitions. This book, based on Geroch's University of Chicago course, will be especially helpful to those working in theoretical physics, including such areas as relativity, particle physics, and astrophysics.
Author: Jan Govaerts Publisher: World Scientific ISBN: 9814488682 Category : Science Languages : en Pages : 503
Book Description
The following topics are discussed in this volume: recent developments in operator theory, coherent states and wavelet analysis, geometric and topological methods in theoretical physics and quantum field theory, and applications of these methods of mathematical physics to problems in atomic and molecular physics as well as the world of the elementary particles and their fundamental interactions. Two extensive sets of lecture notes on quantization techniques in general, and quantum gauge theories and strings as an avenue towards quantum geometry, are also included. The volume should be of interest to anyone working in a field using the mathematical methods associated with any of these topics.