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Differential Geometry For Physicists
This book is divided into fourteen chapters, with 18 appendices as introduction to prerequisite topological and algebraic knowledge, etc. The first seven chapters focus on local analysis. This part can be used as a fundamental textbook for graduate students of theoretical physics. Chapters 8-10 discuss geometry on fibre bundles, which facilitates further reference for researchers. The last four chapters deal with the Atiyah-Singer index theorem, its generalization and its application, quantum anomaly, cohomology field theory and noncommutative geometry, giving the reader a glimpse of the frontier of current research in theoretical physics.
Yang-Baxter Equation and Quantum Enveloping Algebras
This is the first-ever textbook on the Yang-Baxter equation. A key nonlinear equation for solving two important models in many-body statistical theory - the many-body problem in one dimension with repulsive delta-function interaction presented by Professor Baxter in 1972 - it has become one of the main concerns of physicists and mathematicians in the last ten years. A textbook on this subject which also serves as a reference book is vital for an equation which plays important roles in diverse areas of physics and mathematics like the completely integrable statistical models, conformal field theories, topological field theories, the theory of braid groups, the theory of knots and links, etc. ...
Lorentz and Poincar Invariance
This collection of papers provides a broad view of the development of Lorentz and Poincar(r) invariance and spacetime symmetry throughout the past 100 years. The issues explored in these papers include: (1) formulations of relativity theories in which the speed of light is not a universal constant but which are consistent with the four-dimensional symmetry of the Lorentz and Poincar(r) groups and with experimental results, (2) analyses and discussions by Reichenbach concerning the concepts of simultaneity and physical time from a philosophical point of view, and (3) results achieved by the union of the relativity and quantum theories, marking the beginnings of quantum electrodynamics and rel...
Group Theory For Physicists (Second Edition)
This textbook explains the fundamental concepts and techniques of group theory by making use of language familiar to physicists. Calculation methods in the context of physics are emphasized. New materials drawn from the teaching and research experience of the author are included. The generalized Gel'fand's method is presented to calculate the matrices of irreducible representations of the simple Lie algebra and its Clebsch-Gordan coefficients. This book is for graduate students and young researchers in physics, especially theoretical physics. It is also for graduate students in theoretical chemistry.
Group Theory for Physicists
This textbook explains the fundamental concepts and techniques of group theory by making use of language familiar to physicists. Application methods to physics are emphasized. New materials drawn from the teaching and research experience of the author are included. This book can be used by graduate students and young researchers in physics, especially theoretical physics. It is also suitable for some graduate students in theoretical chemistry.
100 Years Of Gravity And Accelerated Frames: The Deepest Insights Of Einstein And Yang-mills
This collection of papers presents ideas and problems arising over the past 100 years regarding classical and quantum gravity, gauge theories of gravity, and spacetime transformations of accelerated frames. Both Einstein's theory of gravity and the Yang-Mills theory are gauge invariant. The invariance principles in physics have transcended both kinetic and dynamic properties and are at the very heart of our understanding of the physical world. In this spirit, this book attempts to survey the development of various formulations for gravitational and Yang-Mills fields and spacetime transformations of accelerated frames, and to reveal their associated problems and limitations.The aim is to pres...
Affine Lie Algebras and Quantum Groups
This is an introduction to the theory of affine Lie Algebras, to the theory of quantum groups, and to the interrelationships between these two fields that are encountered in conformal field theory.
Foundations Of The Hyperunified Field Theory
The quest for the unification of fundamental interactions has become the most challenging frontier of sciences in the 21st century. This book presents a detailed analysis and systematic investigation of the foundations of the hyperunified field theory (HUFT) in light of the path integral formulation with the least action principle. Alternative to other unification theories, the starting point of HUFT is initiated from a simple notion that the universe is made of the fundamental building block which is always moving and obeys the basic rule. Such a rule is delved into in this book by proposing the maximum locally entangled-qubits motion principle together with the scaling and gauge invariance...
Geometric Methods In The Elastic Theory Of Membranes In Liquid Crystal Phases
This book contains a comprehensive description of the mechanical equilibrium and deformation of membranes as a surface problem in differential geometry. Following the pioneering work by W Helfrich, the fluid membrane is seen as a nematic or smectic — A liquid crystal film and its elastic energy form is deduced exactly from the curvature elastic theory of the liquid crystals. With surface variation the minimization of the energy at fixed osmotical pressure and surface tension gives a completely new surface equation in geometry that involves potential interest in mathematics. The investigations of the rigorous solution of the equation that have been carried out in recent years by the authors and their co-workers are presented here, among which the torus and the discocyte (the normal shape of the human red blood cell) may attract attention in cell biology. Within the framework of our mathematical model by analogy with cholesteric liquid crystals, an extensive investigation is made of the formation of the helical structures in a tilted chiral lipid bilayer, which has now become a hot topic in the fields of soft matter and biomembranes.
Special Relativity And Its Experimental Foundation
This book is divided into two parts. In the first part we introduce the foundations of special relativity, such as, the inertial frame of reference, the definition of simulataneity, and Einstein's two basic hypotheses. We give the main relativistic effects, e.g. the relativity of simultaneity, velocity addition, length-contraction, the apparent shape of a moving body, time-dilation, Doppler effect, and the Thomas precession, In particular, the simultaneity problem and slow transport of clocks are investigated in detail by means of the test theories of special relativity. In the second part, variant types of experiments performed up to now are analyzed and compared to the predictions of special relativity. This shows that the experiments are a test of the two-way speed of light, but not of the one-way speed of light.
