The aim of this book is to introduce a graduate student to selected concepts in condensed matter physics for which the language of field theory is ideally suited. The examples considered in this book are those of superfluidity for weakly interacting bosons, collinear magnetism, and superconductivity. Quantum phase transitions are also treated in the context of quantum dissipative junctions and interacting fermions constrained to one-dimensional position space. The style of presentation is sufficiently detailed and comprehensive that it only presumes familiarity with undergraduate physics.
Lecture Notes in Microeconomic Theory is the first publication of Ariel Rubinstein's lecture notes from the first part of his well-known course in microeconomic theory, which he has taught for fifteen years to first-year graduate students at Tel Aviv, Princeton, and New York universities. The book will be an invaluable supplement to primary textbooks in microeconomic theory. Conveying the style and method of Rubinstein's lectures, it will benefit teachers and research economists as well as students. The book focuses on and provides a critical assessment of models of rational economic agents, and it contains a large number of original problems. Rubinstein, one of the world's most-respected economics theorists, has made substantial contributions to several fields in economics, particularly game theory. His work is characterized by an unusual combination of deep originality and surprising simplicity. He is probably best known for his contributions to the bargaining problem and, more recently, to bounded rationality.
This book presents the theory of plates and shells on the basis of the three-dimensional parent theory. The authors explore the thinness of the structure to represent the mechanics of the actual thin three-dimensional body under consideration by a more tractable two-dimensional theory associated with an interior surface. In this way, the relatively complex three-dimensional continuum mechanics of the thin body is replaced by a far more tractable two-dimensional theory. To ensure that the resulting model is predictive, it is necessary to compensate for this ‘dimension reduction’ by assigning additional kinematical and dynamical descriptors to the surface whose deformations are modelled by the simpler two-dimensional theory. The authors avoid the various ad hoc assumptions made in the historical development of the subject, most notably the classical Kirchhoff–Love hypothesis requiring that material lines initially normal to the shell surface remain so after deformation. Instead, such conditions, when appropriate, are here derived rather than postulated.
Intended mainly for advanced graduate students in theoretical physics, this comprehensive volume covers recent advances in string theory and field theory dualities. It is based on the annual lectures given at the School of the Theoretical Advanced Study Institute (2003) a traditional event that brings together graduate students in high energy physics for an intensive course given by leaders in their fields.The first lecture by Paul Aspinwall is a description of branes in Calabi-Yau manifolds, which includes an introduction to the modern ideas of derived categories and their relation to D-branes. Juan Maldacena's second lecture is a short introduction to the AdS/CFT correspondence with a short discussion on its plane wave limit. Tachyon condensation for open strings is discussed in the third lecture by Ashoke Sen while Eva Silverstein provides a useful summary of the various attempts to produce four-dimensional physics out of string theory and M-theory in the fourth lecture. Matthew Strassler's fifth lecture is a careful discussion of a theory that has played a very important role in recent developments in string theory — a quantum field theory that produces a duality cascade which also has a large N gravity description. The sixth lecture by Washington Taylor explains how to perform perturbative computations using string field theory.The written presentation of these lectures is detailed yet straightforward, and they will be of great use to both students and experienced researchers in high energy theoretical physics.
The notion of a motive is an elusive one, like its namesake "the motif" of Cezanne's impressionist method of painting. Its existence was first suggested by Grothendieck in 1964 as the underlying structure behind the myriad cohomology theories in Algebraic Geometry. We now know that there is a triangulated theory of motives, discovered by Vladimir Voevodsky, which suffices for the development of a satisfactory Motivic Cohomology theory. However, the existence of motives themselves remains conjectural. This book provides an account of the triangulated theory of motives. Its purpose is to introduce Motivic Cohomology, to develop its main properties, and finally to relate it to other known invariants of algebraic varieties and rings such as Milnor K-theory, etale cohomology, and Chow groups. The book is divided into lectures, grouped in six parts. The first part presents the definition of Motivic Cohomology, based upon the notion of presheaves with transfers. Some elementary comparison theorems are given in this part. The theory of (etale, Nisnevich, and Zariski) sheaves with transfers is developed in parts two, three, and six, respectively. The theoretical core of the book is the fourth part, presenting the triangulated category of motives. Finally, the comparison with higher Chow groups is developed in part five. The lecture notes format is designed for the book to be read by an advanced graduate student or an expert in a related field. The lectures roughly correspond to one-hour lectures given by Voevodsky during the course he gave at the Institute for Advanced Study in Princeton on this subject in 1999-2000. In addition, many of the original proofs have been simplified and improved so that this book will also be a useful tool for research mathematicians. Information for our distributors: Titles in this series are copublished with the Clay Mathematics Institute (Cambridge, MA).
The inaugural research program of the Institute for Mathematical Sciences at the National University of Singapore took place from July to December 2001 and was devoted to coding theory and cryptology. As part of the program, tutorials for graduate students and junior researchers were given by world-renowned scholars. These tutorials covered fundamental aspects of coding theory and cryptology and were designed to prepare for original research in these areas. The present volume collects the expanded lecture notes of these tutorials. The topics range from mathematical areas such as computational number theory, exponential sums and algebraic function fields through coding-theory subjects such as extremal problems, quantum error-correcting codes and algebraic-geometry codes to cryptologic subjects such as stream ciphers, public-key infrastructures, key management, authentication schemes and distributed system security.
The handbook is divided into four parts: model theory, set theory, recursion theory and proof theory. Each of the four parts begins with a short guide to the chapters that follow. Each chapter is written for non-specialists in the field in question. Mathematicians will find that this book provides them with a unique opportunity to apprise themselves of developments in areas other than their own.
Theoretical and Computational Photochemistry: Fundamentals, Methods, Applications and Synergy with Experimental Approaches provides a comprehensive overview of photoactive systems and photochemical processes. After an introduction to photochemistry, the book discusses the key computational chemistry methods applied to the study of light-induced processes over the past decade, and further outlines recent research topics to which these methods have been applied. By discussing the synergy between experimental and computational data, the book highlights how theoretical studies could facilitate understanding experimental findings. This helpful guide is for both theoretical chemists and experimental photochemistry researchers interested in utilizing computational photochemistry methods for their own work. - Reviews the fundamentals of photochemistry, helping those new to the field in understanding key concepts - Provides detailed guidance and comparison of computational and theoretical methods, highlighting the suitability of each method for different case studies - Outlines current applications to encourage discussion of the synergy between experimental and computational data, and inspiring further application of these methods to other photochemical processes
