Guang-jiong Ni & Su-qing Chen (Fudan Univ)

Advanced Quantum Mechanics

480 pages, 10x7 inches
Fall 2002 Hardcover
ISBN 1-58949-010-X

This book is based on lecture notes developed in last twenty two years during which the authors have been teaching a core graduate course, Quantum Mechanics II, at Fudan University. It covers a very broad range of topics, presenting the state of the art in Quantum Mechanics. Discussions on some topics such as Levinson theorem, Casimir effect, the essence of special relativity, the interpretation of wave function, geometric phase, fractional statistics, and paradoxes in quantum mechanics, reflect to some extent the authors' own research results. The book is profound, practical, enlightening, and pleasantly readable. It is not only a very good textbook for students majoring in theoretical, experimental, or applied physics, but also a very useful reference for researchers as well.

Readership: graduate students, teachers, researchers in (both theoretical and experimental) quantum physics.

CH.1. Basic Concepts and Methods in Quantum Mechanics.
CH.2. Theory of Quantum Scattering.
CH.3. Symmetries and Angular Momentum in Quantum Mechanics.
CH.4. Quantization of Electromagnetic Field and its Interaction with Charged Particles.
CH.5. Density Matrix and Quantum Statistics.
CH.6. Phase in Quantum Mechanics.
CH.7. Motion of Electron in Magnetic Fields.
CH.8. Methods in Quantum Many Body Problems and Applications.
CH.9. Relativistic Quantum Mechanics.
CH.10. Experiments and Interpretation of Quantum Mechanics.
App. Convention units

About Authors:
Guang-jiong Ni is a Chair Professor of Physics in Fudan University, Shanghai. He has been teaching in Fudan for over 45 years and served as the director of Modern Physics Institute and the head of the Division for Theoretical Physics for many years. His research areas include quantum mechanics, field theory, and particle physics. He is the author for over 170 papers published in well known journals. Prof. Ni is a popular writer of science in China. His books Modern Physics (1979), Methods of Mathematical Physics (1989), Levinson Theorem, Anomaly and Phase Transition of Vacuum (1995), Physics Changing the World (1998), and Advanced Quantum Mechanics (2000) receive very warm welcome from very broad range of readers. He has received numerous rewards for his research, teaching activities and book writing.
Su-qing Chen is a Professor of Physics in Fudan University, Shanghai. Before joining the Fudan faculty, she worked as a researcher in Shanghai Institute for Nuclei, mainly in the areas of nuclear theory, until 1978. In Fudan, Prof. Chen taught the courses Quantum Mechanics and Group Theory for many years. Her research work has been in theoretical physics, with more than 20 publications. She is the co-author for two books "Levinson Theorem , Anomaly and Phase Transition of Vacuum " and "Advanced Quantum Mechanics". The former had been awarded the Science and Technology Progress Prize by Education Ministry of China in 1999.
Su-qing married Guang-jiong in 1960, and they have been living a very happy life together since then.

Gordon W. Semenoff
(University of British Columbia)

Introduction to Gauge Theory

300 pages, 10x7 inches
Winter 2002 Hardcover
ISBN 1-58949-008-8

This book is intended as a pedagogical introduction to the subject of the classical and quantum dynamics of gauge fields. It should be accessible to senior undergraduate and beginning graduate students in physics. It assumes that the reader has some background in elementary quantum mechanics and it develops the idea of gauge symmetry from an elementary point of view. The geometrical interpretation of gauge fields is discussed. The formulation of Yang-Mills theory as both a classical and a quantum dynamical system are discussed. Topics of perturbation theory, asymptotic freedom, quark confinement and large N expansions are covered.

Gauge symmetry is at the heart of modern particle physics. It also makes some interesting appearances in condensed matter physics, particularly in the modeling of strongly correlated electrons. In teaching courses in physics both at the undergraduate and graduate level, I have come to the realization that it would be a great advantage to the student to master the concepts of gauge invariance and gauge fields earlier than at the graduate level, which is now standard. For this reason, I have set out to put together this book. It is intended to be a basic introduction to the ideas and some of the structure of gauge field theories. I have attempted, as much as possible, to make it accessible to the physics student who has a basic familiarity with the standard undergraduate physics curriculum, elementary differential equations, classical mechanics, electricity and magnetism, quantum mechanics and the special theory of relativity. This is typical of senior undergraduate physics majors in North American universities. At least the first chapter should be easily readable to such a student. The later chapters which deal with gauge theories as quantum field theories are unavoidably more involved - no matter how you look at it, quantum field theory is a technical subject. Nevertheless, at each opportunity, I have attempted to keep the arguments as simple as possible with the hope that they are understandable to the novice reader.

Larry Wos (Argonne)

The Mining of Missing Treasure

320 pages 10x7 inches w/ CDROM
Fall 2002 Hardcover
ISBN 1-58949-023-1


Most appealing - and sometimes even stirring - is a well-constructed case showing that, without doubt, some given assertion holds. Typically, such a case is based on logical and flawless reasoning, on a sequence of steps that follow inevitably from the hypotheses used to deduce each. In other words, a proof is given establishing that the assertion under consideration indeed holds.

Such proofs are clearly crucial to logic and to mathematics. Not so obvious, but true, proofs are crucial to circuit design, program writing, and, more generally, to various activities in which reasoning plays a vital role. Indeed, most desirable is the case in which no doubt exists regarding the absence of flaws in the design of a chip, in the structure of a computer program, in the argument on which an important decision is based. Such careful reasoning is even the key factor in games that include chess and poker.

This book features one example after another of flawless logical reasoning the context is that of finding proofs absent from the literature. The means for finding the missing proofs is reliance on a single computer program, William McCune's automated reasoning program OTTER.

One motivating force for writing this book is to interest others in automated reasoning, logic and mathematics. As the text strongly indicates, we delight in using OTTER equally in two quite distinct activities: finding a proof where none is offered by the literature, and finding a proof far more appealing than any the literature provides. We believe that many other individuals, if introduced to this program, will also derive substantial enjoyment. Further, we believe that the challenge offered by the type of problem featured in this book can be as engrossing as solving puzzles and playing various games that appeal to the mind. Indeed, sometimes, inexpressible is the excitement engendered when seeking a proof with fewer steps than was found by one of the great minds of the twentieth century. Some proofs are simply beautiful to behold.
A second motivating force resets with our obvious enjoyment of the type of research featured in this book. Like the fancier of fine wines, we continually seek new open questions to attack, whether (at one end of the spectrum) they concern the settling of a conjecture or (at the other end) the focus is on proof betterment. We encourage readers to send us additional open questions and challenging problems.
Another factor that motivated us was our wish to collect in a single volume a surprisingly large number of proofs, most of which were previously absent from the literature. In some cases, no proof was offered of any type; in some cases, the proof that was offered was far from axiomatic. And even where an axiomatic proofs only, some in the text and many more on the included CD-ROM. None of the proofs rely on induction, or on meta argument, or on higher-order logic. In one sense, the book can serve as an encyclopedia of proofs -- many new and many improved - a work that sometimes extends, sometimes replaces, and sometimes supplements the research of more than a century. These proofs offer the implicit challenge of finding others that are further improvements.

In a a rather different sense, the book may serve as the key to eventually answering one open question after another, whether the context is logic, mathematics, design, synthesis, or some other area relying on sound reasoning. In that regards, we include in details numerous diverse methodologies are themselves intriguing. For an example, one methodology asks for two independent paths that lead to success and, rather than emphasizing what is common to both (their intersection), instead heavily focuses on what is not shared (their symmetric difference). A quite different and counterintuitive example (in effect) has the program avoid the attack successfully taken by one of the masters.

Although the emphasis here is on their use in the context of logic and mathematics, we conjecture that the methodologies we offer will prove most useful in a far wider context. We also suspect that, especially for those who enjoy solving puzzles and unraveling the mysteries of sciences, the nature of the methodologies will provide substantial stimulation.

If we succeed, this volume will introduce some readers to the excitement of discovering new results, increase the intrigue of those already familiar with such excitement, and (for the expert) add to the arsenal of weapons for attacking deep questions and hard problems.

M. GOLBERG, Las Vegas, USA and H. A. CHO, University of Nevada, USA

Introduction to Regression Analysis

ISBN: 1-85312-624-1
Published: 2002
Pages: TBA

This book provides an introduction to regression analysis for third-year undergraduate and graduate students in science, engineering, the social sciences and medicine. Emphasis is placed on the classical linear model using least squares estimation and inference, while topics of current interest, such as regression diagnostics, and ridge and logistic regression are also treated.
In contrast to other texts at this level, the theoretical foundation of the subject is presented in some detail based on extensive use of matrix algebra.

V. D. SEREMET, State Agrarian University of Moldova, Republic Of Moldova

Handbook of Green's Functions and Matrices

ISBN: 1-85312-933-X
Published: 2002
Pages: 304pp + CD Rom

In this book the author describes his own technique of constructing Greenfs functions and matrices for the elastostatic Lamefs equations and provides examples of applications in applied mathematical physics.

Designed for graduate and postgraduate students investigating such areas as elasticity, thermoelasticity, mechanics, heat conduction, electro- and magneto conduction, electronics, radio-physics, hydrodynamics, and conduction of moisture, the text will also be of interest to engineers and researchers working in these fields.

Many problems and solutions are included while an accompanying CD-ROM features examples and applications of Greenfs functions for Poissonfs equation, and 2D and 3D Greenfs matrices for Lamefs equations.