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Lecture Notes On Chern Simons Witten Theory
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Book Synopsis Lecture Notes on Chern-Simons-Witten Theory by : Sen Hu
Download or read book Lecture Notes on Chern-Simons-Witten Theory written by Sen Hu and published by World Scientific. This book was released on 2001 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Lectures on Chern-Weil Theory and Witten Deformations by : Weiping Zhang
Download or read book Lectures on Chern-Weil Theory and Witten Deformations written by Weiping Zhang and published by World Scientific. This book was released on 2001 with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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."
Book Synopsis Lectures on Tensor Categories and Modular Functors by : Bojko Bakalov
Download or read book Lectures on Tensor Categories and Modular Functors written by Bojko Bakalov and published by American Mathematical Soc.. This book was released on 2001 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Homotopy Quantum Field Theory by : Vladimir G. Turaev
Download or read book Homotopy Quantum Field Theory written by Vladimir G. Turaev and published by European Mathematical Society. This book was released on 2010 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Lectures on Field Theory and Topology by : Daniel S. Freed
Download or read book Lectures on Field Theory and Topology written by Daniel S. Freed and published by American Mathematical Soc.. This book was released on 2019-08-23 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lectures recount an application of stable homotopy theory to a concrete problem in low energy physics: the classification of special phases of matter. While the joint work of the author and Michael Hopkins is a focal point, a general geometric frame of reference on quantum field theory is emphasized. Early lectures describe the geometric axiom systems introduced by Graeme Segal and Michael Atiyah in the late 1980s, as well as subsequent extensions. This material provides an entry point for mathematicians to delve into quantum field theory. Classification theorems in low dimensions are proved to illustrate the framework. The later lectures turn to more specialized topics in field theory, including the relationship between invertible field theories and stable homotopy theory, extended unitarity, anomalies, and relativistic free fermion systems. The accompanying mathematical explanations touch upon (higher) category theory, duals to the sphere spectrum, equivariant spectra, differential cohomology, and Dirac operators. The outcome of computations made using the Adams spectral sequence is presented and compared to results in the condensed matter literature obtained by very different means. The general perspectives and specific applications fuse into a compelling story at the interface of contemporary mathematics and theoretical physics.
Book Synopsis Frobenius Algebras and 2-D Topological Quantum Field Theories by : Joachim Kock
Download or read book Frobenius Algebras and 2-D Topological Quantum Field Theories written by Joachim Kock and published by Cambridge University Press. This book was released on 2004 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 2003 book describes a striking connection between topology and algebra, namely that 2D topological quantum field theories are equivalent to commutative Frobenius algebras. The precise formulation of the theorem and its proof is given in terms of monoidal categories, and the main purpose of the book is to develop these concepts from an elementary level, and more generally serve as an introduction to categorical viewpoints in mathematics. Rather than just proving the theorem, it is shown how the result fits into a more general pattern concerning universal monoidal categories for algebraic structures. Throughout, the emphasis is on the interplay between algebra and topology, with graphical interpretation of algebraic operations, and topological structures described algebraically in terms of generators and relations. The book will prove valuable to students or researchers entering this field who will learn a host of modern techniques that will prove useful for future work.
Book Synopsis The Seiberg-Witten Equations and Applications to the Topology of Smooth Four-Manifolds. (MN-44), Volume 44 by : John W. Morgan
Download or read book The Seiberg-Witten Equations and Applications to the Topology of Smooth Four-Manifolds. (MN-44), Volume 44 written by John W. Morgan and published by Princeton University Press. This book was released on 2014-09-08 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: The recent introduction of the Seiberg-Witten invariants of smooth four-manifolds has revolutionized the study of those manifolds. The invariants are gauge-theoretic in nature and are close cousins of the much-studied SU(2)-invariants defined over fifteen years ago by Donaldson. On a practical level, the new invariants have proved to be more powerful and have led to a vast generalization of earlier results. This book is an introduction to the Seiberg-Witten invariants. The work begins with a review of the classical material on Spin c structures and their associated Dirac operators. Next comes a discussion of the Seiberg-Witten equations, which is set in the context of nonlinear elliptic operators on an appropriate infinite dimensional space of configurations. It is demonstrated that the space of solutions to these equations, called the Seiberg-Witten moduli space, is finite dimensional, and its dimension is then computed. In contrast to the SU(2)-case, the Seiberg-Witten moduli spaces are shown to be compact. The Seiberg-Witten invariant is then essentially the homology class in the space of configurations represented by the Seiberg-Witten moduli space. The last chapter gives a flavor for the applications of these new invariants by computing the invariants for most Kahler surfaces and then deriving some basic toological consequences for these surfaces.
Book Synopsis Chern-simons (Super)gravity by : Mokhtar Hassaine
Download or read book Chern-simons (Super)gravity written by Mokhtar Hassaine and published by World Scientific. This book was released on 2016-01-07 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'The authors provide an up-to-date, well-organised background and essential elements of supergravity notions as well as all relevant aspects of Chern-Simons forms in gravitation. The book is a self-contained, informative, and much-needed broad introduction into the latest quantum gravity concepts, with a main focus on Chern-Simons gravity and supersymmetry … The book represents a comprehensive and systematic pedagogical exposition on gravitational Chern-Simons (Super)gravity theories, their applications, together with a selection of related recent developments in the field.'Contemporary PhysicsThis 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.
Book Synopsis Current Algebra and Anomalies by : Sam Treiman
Download or read book Current Algebra and Anomalies written by Sam Treiman and published by Princeton University Press. This book was released on 2014-07-14 with total page 550 pages. Available in PDF, EPUB and Kindle. Book excerpt: Current algebra remains our most successful analysis of fundamental particle interactions. This collection of surveys on current algebra and anomalies is a successor volume to Lectures on Current Algebra and Its Applications (Princeton Series in Physics, 1972). Originally published in 1986. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Book Synopsis Differential Forms in Algebraic Topology by : Raoul Bott
Download or read book Differential Forms in Algebraic Topology written by Raoul Bott and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: Developed from a first-year graduate course in algebraic topology, this text is an informal introduction to some of the main ideas of contemporary homotopy and cohomology theory. The materials are structured around four core areas: de Rham theory, the Cech-de Rham complex, spectral sequences, and characteristic classes. By using the de Rham theory of differential forms as a prototype of cohomology, the machineries of algebraic topology are made easier to assimilate. With its stress on concreteness, motivation, and readability, this book is equally suitable for self-study and as a one-semester course in topology.
Book Synopsis Quantum Fields and Strings: A Course for Mathematicians by : Pierre Deligne
Download or read book Quantum Fields and Strings: A Course for Mathematicians written by Pierre Deligne and published by American Mathematical Society. This book was released on 1999-10-25 with total page 801 pages. Available in PDF, EPUB and Kindle. Book excerpt: A run-away bestseller from the moment it hit the market in late 1999. This impressive, thick softcover offers mathematicians and mathematical physicists the opportunity to learn about the beautiful and difficult subjects of quantum field theory and string theory. Cover features an intriguing cartoon that will bring a smile to its intended audience.
Book Synopsis Lectures at Knots '96 by : S. Suzuki
Download or read book Lectures at Knots '96 written by S. Suzuki and published by World Scientific. This book was released on 1997 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of ten lectures given at an international workshop/conference on knot theory held in July 1996 at Waseda University Conference Center. It was organised by the International Research Institute of Mathematical Society of Japan. The workshop was attended by nearly 170 mathematicians from Japan and 14 other countries, most of whom were specialists in knot theory. The lectures can serve as an introduction to the field for advanced undergraduates, graduates and also researchers working in areas such as theoretical physics.
Book Synopsis Chern-Simons Gauge Theory: 20 Years After by : Jørgen E. Andersen
Download or read book Chern-Simons Gauge Theory: 20 Years After written by Jørgen E. Andersen and published by American Mathematical Soc.. This book was released on 2011 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author :Bernhelm Booß-Bavnbek Publisher :Springer Science & Business Media ISBN 13 :3642118968 Total Pages :372 pages Book Rating :4.6/5 (421 download)
Book Synopsis New Paths Towards Quantum Gravity by : Bernhelm Booß-Bavnbek
Download or read book New Paths Towards Quantum Gravity written by Bernhelm Booß-Bavnbek and published by Springer Science & Business Media. This book was released on 2010-06-04 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aside from the obvious statement that it should be a theory capable of unifying general relativity and quantum field theory, not much is known about the true nature of quantum gravity. New ideas - and there are many of them for this is an exciting field of research - often diverge to a degree where it seems impossible to decide in which of the many possible direction(s) the ongoing developments should be further sustained. The division of the book in two (overlapping) parts reflects the duality between the physical vision and the mathematical construction. The former is represented by tutorial reviews on non-commutative geometry, on space-time discretization and renormalization and on gauge field path integrals. The latter one by lectures on cohomology, on stochastic geometry and on mathematical tools for the effective action in quantum gravity. The book will benefit everyone working or entering the field of quantum gravity research.
Book Synopsis Enumerative Invariants in Algebraic Geometry and String Theory by : Marcos Marino
Download or read book Enumerative Invariants in Algebraic Geometry and String Theory written by Marcos Marino and published by Springer. This book was released on 2008-08-15 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: Starting in the middle of the 80s, there has been a growing and fruitful interaction between algebraic geometry and certain areas of theoretical high-energy physics, especially the various versions of string theory. Physical heuristics have provided inspiration for new mathematical definitions (such as that of Gromov-Witten invariants) leading in turn to the solution of problems in enumerative geometry. Conversely, the availability of mathematically rigorous definitions and theorems has benefited the physics research by providing the required evidence in fields where experimental testing seems problematic. The aim of this volume, a result of the CIME Summer School held in Cetraro, Italy, in 2005, is to cover part of the most recent and interesting findings in this subject.
Book Synopsis Dirichlet Branes and Mirror Symmetry by :
Download or read book Dirichlet Branes and Mirror Symmetry written by and published by American Mathematical Soc.. This book was released on 2009 with total page 698 pages. Available in PDF, EPUB and Kindle. Book excerpt: Research in string theory has generated a rich interaction with algebraic geometry, with exciting work that includes the Strominger-Yau-Zaslow conjecture. This monograph builds on lectures at the 2002 Clay School on Geometry and String Theory that sought to bridge the gap between the languages of string theory and algebraic geometry.
Book Synopsis Topology And Physics by : Chen Ning Yang
Download or read book Topology And Physics written by Chen Ning Yang and published by World Scientific. This book was released on 2019-01-09 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'The book is an engaging and influential collection of significant contributions from an assembly of world expert leaders and pioneers from different fields, working at the interface between topology and physics or applications of topology to physical systems … The book explores many interesting and novel topics that lie at the intersection between gravity, quantum fields, condensed matter, physical cosmology and topology … A rich, well-organized, and comprehensive overview of remarkable and insightful connections between physics and topology is here made available to the physics reader.'Contemporary PhysicsSince its birth in Poincaré's seminal 1894 'Analysis Situs', topology has become a cornerstone of mathematics. As with all beautiful mathematical concepts, topology inevitably — resonating with that Wignerian principle of the effectiveness of mathematics in the natural sciences — finds its prominent role in physics. From Chern-Simons theory to topological quantum field theory, from knot invariants to Calabi-Yau compactification in string theory, from spacetime topology in cosmology to the recent Nobel Prize winning work on topological insulators, the interactions between topology and physics have been a triumph over the past few decades.In this eponymous volume, we are honoured to have contributions from an assembly of grand masters of the field, guiding us with their world-renowned expertise on the subject of the interplay between 'Topology' and 'Physics'. Beginning with a preface by Chen Ning Yang on his recollections of the early days, we proceed to a novel view of nuclei from the perspective of complex geometry by Sir Michael Atiyah and Nick Manton, followed by an entrée toward recent developments in two-dimensional gravity and intersection theory on the moduli space of Riemann surfaces by Robbert Dijkgraaf and Edward Witten; a study of Majorana fermions and relations to the Braid group by Louis H Kauffman; a pioneering investigation on arithmetic gauge theory by Minhyong Kim; an anecdote-enriched review of singularity theorems in black-hole physics by Sir Roger Penrose; an adventure beyond anyons by Zhenghan Wang; an aperçu on topological insulators from first-principle calculations by Haijun Zhang and Shou-Cheng Zhang; finishing with synopsis on quantum information theory as one of the four revolutions in physics and the second quantum revolution by Xiao-Gang Wen. We hope that this book will serve to inspire the research community.
