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Fermions and Anomalies in Quantum Field Theories
This book presents a modern view of anomalies in quantum field theories. It is divided into six parts. The first part is preparatory covering an introduction to fermions, a description of the classical symmetries, and a short introduction to conformal symmetry. The second part of the book is devoted to the relation between anomalies and cohomology. The third part deals with perturbative methods to compute gauge, diffeomorphism and trace anomalies. In the fourth part the same anomalies are calculated with non-perturbative heat-kernel-like methods. Part five is devoted to the family's index theorem and its application to chiral anomalies, and to the differential characters and their applications to global anomalies. Part six is devoted to special topics including a complete calculation of trace and diffeomorphism anomalies of a Dirac fermion in a MAT background in two dimensions, Wess-Zumino terms in field theories, sigma models, their local and global anomalies and their cancelation, and finally the analysis of the worldsheet, sigma model, and target space anomalies of string and superstring theories. The book is targeted to researchers and graduate students.
Physics Of Heavy Fermions: Heavy Fermions And Strongly Correlated Electrons Systems
A large variety of materials prove to be fascinating in solid state and condensed matter physics. New materials create new physics, which is spearheaded by the international experimental expert, Prof Yoshichika Onuki. Among them, the f electrons of rare earth and actinide compounds typically exhibit a variety of characteristic properties, including spin and charge orderings, spin and valence fluctuations, heavy fermions, and anisotropic superconductivity. These are mainly manifestations of better competitive phenomena between the RKKY interaction and the Kondo effect. The present text is written so as to understand these phenomena and the research they prompt. For example, superconductivity was once regarded as one of the more well-understood many-body problems. However, it is, in fact, still an exciting phenomenon in new materials. Additionally, magnetism and superconductivity interplay strongly in heavy fermion superconductors. The understanding of anisotropic superconductivity and magnetism is a challenging problem in solid state and condensed matter physics. This book will tackle all these topics and more.
Lattice Fermions and Structure of the Vacuum
Among the key problems in modern field theory are the formulation of chiral group theories on the lattice and the quantitative understanding of the quark confinement mechanism. The two topics are closely related by the fact that the chiral nature of the fermions as well as the confinement force are largely topological in origin. Recent advances in this field are here reviewed by some of the world's experts.
Strongly Correlated Fermions and Bosons in Low-Dimensional Disordered Systems
The physics of strongly correlated fermions and bosons in a disordered envi ronment and confined geometries is at the focus of intense experimental and theoretical research efforts. Advances in material technology and in low temper ature techniques during the last few years led to the discoveries of new physical of atomic gases and a possible metal phenomena including Bose condensation insulator transition in two-dimensional high mobility electron structures. Situ ations were the electronic system is so dominated by interactions that the old concepts of a Fermi liquid do not necessarily make a good starting point are now routinely achieved. This is particularly true in the theory of low dime...
Quantum Mechanics, Volume 3
This new, third volume of Cohen-Tannoudji's groundbreaking textbook covers advanced topics of quantum mechanics such as uncorrelated and correlated identical particles, the quantum theory of the electromagnetic field, absorption, emission and scattering of photons by atoms, and quantum entanglement. Written in a didactically unrivalled manner, the textbook explains the fundamental concepts in seven chapters which are elaborated in accompanying complements that provide more detailed discussions, examples and applications. * Completing the success story: the third and final volume of the quantum mechanics textbook written by 1997 Nobel laureate Claude Cohen-Tannoudji and his colleagues Bernard...
Composite Fermions
One of the most exciting recent developments to have emerged from the quantum Hall effect is the subject of composite fermions. This important volume gives a self-contained, comprehensive description of the subject, including fundamentals, more advanced theoretical work, and results from experimental observations of composite fermions.
Bosonization of Interacting Fermions in Arbitrary Dimensions
The author presents in detail a new non-perturbative approach to the fermionic many-body problem, improving the bosonization technique and generalizing it to dimensions d1 via functional integration and Hubbard--Stratonovich transformations. In Part I he clearly illustrates the approximations and limitations inherent in higher-dimensional bosonization and derives the precise relation with diagrammatic perturbation theory. He shows how the non-linear terms in the energy dispersion can be systematically included into bosonization in arbitrary d, so that in d1 the curvature of the Fermi surface can be taken into account. Part II gives applications to problems of physical interest. The book addresses researchers and graduate students in theoretical condensed matter physics.
Composite Fermions
This book was first published in 2007. When electrons are confined to two dimensions, cooled to near absolute zero temperature, and subjected to a strong magnetic field, they form an exotic new collective state of matter. Investigations into this began with the observations of integral and fractional quantum Hall effects, which are among the most important discoveries in condensed matter physics. The fractional quantum Hall effect and a stream of other unexpected findings are explained by a new class of particles: composite fermions. This textbook is a self-contained, pedagogical introduction to the physics and experimental manifestations of composite fermions. Ideal for graduate students and academic researchers, it contains numerous exercises to reinforce the concepts presented. The topics covered include the integral and fractional quantum Hall effects, the composite-fermion Fermi sea, various kinds of excitations, the role of spin, edge state transport, electron solid, bilayer physics, fractional braiding statistics and fractional local charge.
The Kondo Problem to Heavy Fermions
The behaviour of magnetic impurities in metals has posed problems to challenge the condensed matter theorist over the past 30 years. This book deals with the concepts and techniques which have been developed to meet this challenge, and with their application to the interpretation of experiments. This book will be of interest to condensed matter physicists, particularly those interested in strong correlation problems. The detailed discussions of advanced many-body techniques should make it of interest to theoretical physicists in general.
