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Lecture Notes on Chern-Simons-Witten Theory by Sen Hu,E. Witten Pdf
This monograph is based on lectures on topological quantum field theory given in 1989 at Princeton University by E. Witten, in which he unified several important mathematical works in terms of the Donaldson polynomial, Gromov/Floer homology, and Jones polynomials. Witten explained his three-dimensional construction of Jones polynomials, "an elegant construction of a new polynomial invariant in three-dimensional space" (per the author), via quantization of Chern-Simons gauge theory. Hu (Princeton U.) adds missing details and some new developments in the field. Annotation copyrighted by Book News Inc., Portland, OR.
Self-Dual Chern-Simons Theories by Gerald Dunne Pdf
Self-duality greatly reduces the mathematical difficulties of a theory but it is also a notion of considerable physical significance. The new class of self-dual Chern-Simons theories discussed in detail in this book arise in the context of anyonic quantum field theory and have applications to models such as the quantum Hall effect, anyonic superconductivity, and Aharonov-Bohm scattering. There are also interesting connections with the theory of integrable models. The author presents the abelian and non-abelian models for relativistic and non-relativistic realizations of the self-dual Chern-Simons theories and finishes with some applications in quantum physics. The book is written for advanced students and researchers in mathematical, particle, and condensed matter physics.
Lectures on Chern-Weil Theory and Witten Deformations by Weiping Zhang Pdf
This invaluable book is based on the notes of a graduate course on differential geometry which the author gave at the Nankai Institute of Mathematics. It consists of two parts: the first part contains an introduction to the geometric theory of characteristic classes due to ShiingOCoshen Chern and Andr(r) Weil, as well as a proof of the GaussOCoBonnetOCoChern theorem based on the MathaiOCoQuillen construction of Thom forms; the second part presents analytic proofs of the Poincar(r)OCoHopf index formula, as well as the Morse inequalities based on deformations introduced by Edward Witten. Contents: ChernOCoWeil Theory for Characteristic Classes; Bott and DuistermaatOCoHeckman Formulas; GaussOCoBonnetOCoChern Theorem; Poincar(r)OCoHopf Index Formula: An Analytic Proof; Morse Inequalities: An Analytic Proof; ThomOCoSmale and Witten Complexes; Atiyah Theorem on Kervaire Semi-characteristic. Readership: Graduate students and researchers in differential geometry, topology and mathematical physics."
Chern-Simons Gauge Theory: 20 Years After by Jørgen E. Andersen,Jørgen Ellegaard Andersen Pdf
In 1989, Edward Witten discovered a deep relationship between quantum field theory and knot theory, and this beautiful discovery created a new field of research called Chern-Simons theory. This field has the remarkable feature of intertwining a large number of diverse branches of research in mathematics and physics, among them low-dimensional topology, differential geometry, quantum algebra, functional and stochastic analysis, quantum gravity, and string theory. The 20-year anniversary of Witten's discovery provided an opportunity to bring together researchers working in Chern-Simons theory for a meeting, and the resulting conference, which took place during the summer of 2009 at the Max Planck Institute for Mathematics in Bonn, included many of the leading experts in the field. This volume documents the activities of the conference and presents several original research articles, including another monumental paper by Witten that is sure to stimulate further activity in this and related fields. This collection will provide an excellent overview of the current research directions and recent progress in Chern-Simons gauge theory.
Topics in Contemporary Mathematical Physics by Kai Shue Lam Pdf
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.
Topics in Contemporary Mathematical Physics by Kai S Lam Pdf
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.
The International Symposium on Frontiers of Science was held to celebrate the 80th birthday of Chen Ning Yang, one of the great physicists of the 20th century and arguably the most-admired living scientist in China today. Many of the world's great scientists — including sixteen Nobel laureates, Fields medallists and Wolf Prize winners — converged on Beijing from all corners of the globe to pay tribute to Professor Yang. The Symposium was organized by Tsinghua University, with which Professor Yang has had a lifelong relationship. In 1997, he helped to found the Center for Advanced Study at Tsinghua, was appointed to the university's faculty, and has since devoted his energy to the growth of the Center. This unique and invaluable birthday volume is a collection of the presentations made at the Symposium, including fifteen plenary talks, seven of which are by Nobel laureates. It covers a wide range of topics and mirrors Professor Yang's research and intellectual interests. The range of fields encompasses high-energy, condensed-matter, mathematical, applied, bio-, astro-, atomic and quantum physics. Also included are talks given at the birthday banquet. About C N Yang Born in 1922 in Anwhei, China, C N Yang was brought up in the academic atmosphere of Tsinghua University in Beijing, where his father was a professor of mathematics. He received his college education at the National Southwest Associated University in Kunming, China, and completed his BSc there in 1942. His MSc was received in 1944 from Tsinghua University. He entered the University of Chicago in 1946, where he came under the strong influence of Prof E Fermi. After receiving his PhD in 1948, Prof Yang served for a year at the University of Chicago as an instructor. Since 1949 he has been associated with the Institute for Advanced Study, Princeton, where he became a professor in 1955. Prof Yang has worked on various subjects in physics, but is mainly interested in statistical mechanics and symmetry principles. He is a prolific author, his numerous articles appearing in the Bulletin of the American Mathematical Society, The Physical Review, Reviews of Modern Physics and the Chinese Journal of Physics. Prof Yang won the Nobel Prize in Physics in 1957, jointly with T-D Lee. He has been elected a Fellow of the American Physical Society and of Academia Sinica. Contents:Nobel Laureates and Wolf Prize WinnerThe Laser — What It Is and How It Happened (C H Townes, Nobel laureate Berkeley)Neutrino Physics (R L Moessbauer, Nobel laureate Muenchen)Gauge Theory at Tsinghua (S-S Chern, Wolf Prize winner Nankai University & Berkeley)Emergent Relativity (R B Laughlin, Nobel laureate Stanford)Watching Molecular Systems Work, One at a Time (S Chu, Nobel laureate Stanford)The Hidden Information in the Standard Model (G 't Hooft, Nobel laureate Utrecht)Bose–Einstein Condensation in a Dilute Gas the First 70 Years and Some Recent Experiments (E A Cornell & C E Wieman, Nobel laureates Colorado)Production of a Bose–Einstein Condensate of Metastable Helium Atoms (C Cohen-Tannoudji, Nobel laureate College de France)Other Plenary SpeakersFunctional Analysis of the Human Genome: Study of Genetic Disease (L-C Tsui, Toronto)Angle-Resolved Photoemission Spectroscopy Studies of Cuprate Superconductors (Z-X Shen, Stanford University)Superconductivity in 4-Angstrom Carbon Nanotubes (P Sheng, Hong Kong University of Science and Technology)Understanding High Tc Superconductivity (Z-Y Weng, Tsinghua University)Some Reflections on the Mechanization of Mental Labor in the Computer Age (W-T Wu, Academia Sinica)Research and Development Towards X-Ray Free Electron Lasers (L H Yu, Brookhaven National Laboratory)Imaging the Quantum World Using the Phase of Electron Waves (A Tonomura, Hitachi)Papers from Parallel Sessions, and Speeches Readership: Researchers in physics. Keywords:Science;Physics;C N Yang;High Energy Physics;Condensed Matter Physics
Chern-Simons (super) Gravity by Mokhtar Hassaine,Jorge Zanelli Pdf
This book grew out of a set of lecture notes on gravitational Chern-Simons (CS) theories developed over the past decade for several schools and different audiences including graduate students and researchers. CS theories are gauge-invariant theories that can include gravity consistently. They are only defined in odd dimensions and represent a very special class of theories in the Lovelock family. Lovelock gravitation theories are the natural extensions of General Relativity for dimensions greater than four that yield second-order field equations for the metric. These theories also admit local supersymmetric extensions where supersymmetry is an off-shell symmetry of the action, as in a standard gauge theory. Apart from the arguments of mathematical elegance and beauty, the gravitational CS actions are exceptionally endowed with physical attributes that suggest the viability of a quantum interpretation. CS theories are gauge-invariant, scale-invariant and background independent; they have no dimensional coupling constants. All constants in the Lagrangian are fixed rational coefficients that cannot be adjusted without destroying gauge invariance. This exceptional status of CS systems makes them classically interesting to study, and quantum mechanically intriguing and promising.
Lectures on Tensor Categories and Modular Functors by Bojko Bakalov,Alexander A. Kirillov Pdf
This book gives an exposition of the relations among the following three topics: monoidal tensor categories (such as a category of representations of a quantum group), 3-dimensional topological quantum field theory, and 2-dimensional modular functors (which naturally arise in 2-dimensional conformal field theory). The following examples are discussed in detail: the category of representations of a quantum group at a root of unity and the Wess-Zumino-Witten modular functor. The idea that these topics are related first appeared in the physics literature in the study of quantum field theory. Pioneering works of Witten and Moore-Seiberg triggered an avalanche of papers, both physical and mathematical, exploring various aspects of these relations. Upon preparing to lecture on the topic at MIT, however, the authors discovered that the existing literature was difficult and that there were gaps to fill. The text is wholly expository and finely succinct. It gathers results, fills existing gaps, and simplifies some proofs. The book makes an important addition to the existing literature on the topic. It would be suitable as a course text at the advanced-graduate level.
Proceedings of the International Symposium on Frontiers of Science by Chen Ning Yang,Hwa-Tung Nieh Pdf
The International Symposium on Frontiers of Science was held to celebrate the 80th birthday of Chen Ning Yang, one of the great physicists of the 20th century and arguably the most-admired living scientist in China today. Many of the world's great scientists ? including sixteen Nobel laureates, Fields medallists and Wolf Prize winners ? converged on Beijing from all corners of the globe to pay tribute to Professor Yang.The Symposium was organized by Tsinghua University, with which Professor Yang has had a lifelong relationship. In 1997, he helped to found the Center for Advanced Study at Tsinghua, was appointed to the university's faculty, and has since devoted his energy to the growth of the Center.This unique and invaluable birthday volume is a collection of the presentations made at the Symposium, including fifteen plenary talks, seven of which are by Nobel laureates. It covers a wide range of topics and mirrors Professor Yang's research and intellectual interests. The range of fields encompasses high-energy, condensed-matter, mathematical, applied, bio-, astro-, atomic and quantum physics. Also included are talks given at the birthday banquet.About C N YangBorn in 1922 in Anwhei, China, C N Yang was brought up in the academic atmosphere of Tsinghua University in Beijing, where his father was a professor of mathematics. He received his college education at the National Southwest Associated University in Kunming, China, and completed his BSc there in 1942. His MSc was received in 1944 from Tsinghua University. He entered the University of Chicago in 1946, where he came under the strong influence of Prof E Fermi. After receiving his PhD in 1948, Prof Yang served for a year at the University of Chicago as an instructor. Since 1949 he has been associated with the Institute for Advanced Study, Princeton, where he became a professor in 1955.Prof Yang has worked on various subjects in physics, but is mainly interested in statistical mechanics and symmetry principles. He is a prolific author, his numerous articles appearing in the Bulletin of the American Mathematical Society, The Physical Review, Reviews of Modern Physics and the Chinese Journal of Physics.Prof Yang won the Nobel Prize in Physics in 1957, jointly with T-D Lee. He has been elected a Fellow of the American Physical Society and of Academia Sinica.
Homotopy Quantum Field Theory by Vladimir G. Turaev Pdf
Homotopy Quantum Field Theory (HQFT) is a branch of Topological Quantum Field Theory founded by E. Witten and M. Atiyah. It applies ideas from theoretical physics to study principal bundles over manifolds and, more generally, homotopy classes of maps from manifolds to a fixed target space. This book is the first systematic exposition of Homotopy Quantum Field Theory. It starts with a formal definition of an HQFT and provides examples of HQFTs in all dimensions. The main body of the text is focused on $2$-dimensional and $3$-dimensional HQFTs. A study of these HQFTs leads to new algebraic objects: crossed Frobenius group-algebras, crossed ribbon group-categories, and Hopf group-coalgebras. These notions and their connections with HQFTs are discussed in detail. The text ends with several appendices including an outline of recent developments and a list of open problems. Three appendices by M. Muger and A. Virelizier summarize their work in this area. The book is addressed to mathematicians, theoretical physicists, and graduate students interested in topological aspects of quantum field theory. The exposition is self-contained and well suited for a one-semester graduate course. Prerequisites include only basics of algebra and topology.
Topics in Contemporary Mathematical Physics by Kai S Lam Pdf
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.
Low-dimensional Quantum Field Theories For Condensed Matter Physicists - Lecture Notes Of Ictp Summer Course by Lu Yu,Stig Lundqvist,Giuseppe Morandi Pdf
This volume contains a set of pedagogical reviews covering the most recent applications of low-dimensional quantum field theory in condensed matter physics, written by experts who have made major contributions to this rapidly developing field of research. The main purpose is to introduce active young researchers to new ideas and new techniques which are not covered by the standard textbooks.
