Download or read book Kahler Geometry of Loop Spaces written by Armen G. Sergeev and published by . This book was released on 2008 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Kahler geometry of loop spaces written by Armen Sergeev and published by Mathematical Society Of Japan Memoirs. This book was released on 2010-05 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book we study three important classes of infinite-dimensional KÄhler manifolds - loop spaces of compact Lie groups, TeichmÜller spaces of complex structures on loop spaces, and Grassmannians of Hilbert spaces. Each of these manifolds has a rich KÄhler geometry, considered in the first part of the book, and may be considered as a universal object in a category, containing all its finite-dimensional counterparts. On the other hand, these manifolds are closely related to string theory. This motivates our interest in their geometric quantization presented in the second part of the book together with a brief survey of geometric quantization of finite-dimensional KÄhler manifolds. The book is provided with an introductory chapter containing basic notions on infinite-dimensional Frechet manifolds and Frechet Lie groups. It can also serve as an accessible introduction to KÄhler geometry of infinite-dimensional complex manifolds with special attention to the aforementioned three particular classes. It may be interesting for mathematicians working with infinite-dimensional complex manifolds and physicists dealing with string theory. Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets
Download or read book Loop Spaces Characteristic Classes and Geometric Quantization written by Jean-Luc Brylinski and published by Springer Science & Business Media. This book was released on 2009-12-30 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book examines the differential geometry of manifolds, loop spaces, line bundles and groupoids, and the relations of this geometry to mathematical physics. Applications presented in the book involve anomaly line bundles on loop spaces and anomaly functionals, central extensions of loop groups, Kähler geometry of the space of knots, and Cheeger--Chern--Simons secondary characteristics classes. It also covers the Dirac monopole and Dirac’s quantization of the electrical charge.
Download or read book String Theory as the K hler Geometry of Loop Space written by Mark J. Bowick and published by . This book was released on 1987 with total page 4 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Analysis of Random Phenomena written by Ana Bela Cruzeiro and published by World Scientific. This book was released on 2007 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume highlights recent developments of stochastic analysis with a wide spectrum of applications, including stochastic differential equations, stochastic geometry, and nonlinear partial differential equations.While modern stochastic analysis may appear to be an abstract mixture of classical analysis and probability theory, this book shows that, in fact, it can provide versatile tools useful in many areas of applied mathematics where the phenomena being described are random. The geometrical aspects of stochastic analysis, often regarded as the most promising for applications, are specially investigated by various contributors to the volume.
Download or read book Complex Differential Geometry and Supermanifolds in Strings and Fields written by Petrus J.M. Bongaarts and published by Springer. This book was released on 1988-10-12 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume deals with one of the most active fields of research in mathematical physics: the use of geometric and topological methods in field theory. The emphasis in these proceedings is on complex differential geometry, in particular on Kähler manifolds, supermanifolds, and graded manifolds. From the point of view of physics the main topics were field theory, string theory and problems from elementary particle theory involving supersymmetry. The lectures show a remarkable unity of approach and are considerably related to each other. They should be of great value to researchers and graduate students.
Download or read book Complex Monge Amp re Equations and Geodesics in the Space of K hler Metrics written by Vincent Guedj and published by Springer Science & Business Media. This book was released on 2012-01-06 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of these lecture notes is to provide an introduction to the theory of complex Monge–Ampère operators (definition, regularity issues, geometric properties of solutions, approximation) on compact Kähler manifolds (with or without boundary). These operators are of central use in several fundamental problems of complex differential geometry (Kähler–Einstein equation, uniqueness of constant scalar curvature metrics), complex analysis and dynamics. The topics covered include, the Dirichlet problem (after Bedford–Taylor), Monge–Ampère foliations and laminated currents, polynomial hulls and Perron envelopes with no analytic structure, a self-contained presentation of Krylov regularity results, a modernized proof of the Calabi–Yau theorem (after Yau and Kolodziej), an introduction to infinite dimensional riemannian geometry, geometric structures on spaces of Kähler metrics (after Mabuchi, Semmes and Donaldson), generalizations of the regularity theory of Caffarelli–Kohn–Nirenberg–Spruck (after Guan, Chen and Blocki) and Bergman approximation of geodesics (after Phong–Sturm and Berndtsson). Each chapter can be read independently and is based on a series of lectures by R. Berman, Z. Blocki, S. Boucksom, F. Delarue, R. Dujardin, B. Kolev and A. Zeriahi, delivered to non-experts. The book is thus addressed to any mathematician with some interest in one of the following fields, complex differential geometry, complex analysis, complex dynamics, fully non-linear PDE's and stochastic analysis.
Download or read book Infinite Dimensional Algebras and Quantum Integrable Systems written by Petr P. Kulish and published by Springer Science & Business Media. This book was released on 2006-01-17 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the invited lectures of the workshop "Infinite Dimensional Algebras and Quantum Integrable Systems" held in July 2003 at the University of Algarve, Faro, Portugal, as a satellite workshop of the XIV International Congress on Mathematical Physics. In it, recent developments in the theory of infinite dimensional algebras, and their applications to quantum integrable systems, are reviewed by leading experts in the field.
Download or read book Topological Geometrodynamics written by Matti Pitkanen and published by Bentham Science Publishers. This book was released on 2016-03-03 with total page 1235 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topological geometrodynamics (TGD) is a modification of the theory of general relativity inspired by the problems related to the definition of inertial and gravitational energies in the earlier hypotheses. TGD is also a generalization of super string models. TGD brings forth an elegant theoretical projection of reality and builds upon the work by renowned scientists (Wheeler, Feynman, Penrose, Einstein, Josephson to name a few). In TGD, Physical space-time planes are visualized as four-dimensional surfaces in a certain 8-dimensional space (H). The choice of H is fixed by symmetries of standard model and leads to a geometric mapping of known classical fields and elementary particle numbers. TGD differs from Einstein’s geometrodynamics in the way space-time planes or ‘sheets’ are lumped together. Extending the theory based on fusing number concepts implies a further generalisation of the space-time concept allowing the identification of space-time correlates of cognition and intentionality. Additionally, zero energy ontology forces an extension of quantum measurement theory to a theory of consciousness and a hierarchy of phases is identified. Dark matter is thus predicted with far reaching implications for the understanding of consciousness and living systems. Therefore, it sets a solid foundation for modeling our universe in geometric terms. Topological Geometrodynamics: An Overview explains basic and advanced concepts about TGD. The book covers introductory information and classical TGD concepts before delving into twistor-space theory, particle physics, infinite-dimensional spinor geometry, generalized number theory, Planck constants, and the applications of TGD theory in research. The book is a valuable guide to TDG theory for researchers and advanced graduates in theoretical physics and cosmology.
Download or read book The geometry of iterated loop spaces written by J. P. May and published by . This book was released on 1971 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Differential Geometry Geometry in Mathematical Physics and Related Topics written by Robert Everist Greene and published by American Mathematical Soc.. This book was released on 1993 with total page 681 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second of three parts comprising Volume 54, the proceedings of the Summer Research Institute on Differential Geometry, held at the University of California, Los Angeles, July 1990 (ISBN for the set is 0-8218-1493-1). Among the subjects of Part 2 are gauge theory, symplectic geometry, complex ge
Download or read book Current Algebras and Groups written by Jouko Mickelsson and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let M be a smooth manifold and G a Lie group. In this book we shall study infinite-dimensional Lie algebras associated both to the group Map(M, G) of smooth mappings from M to G and to the group of dif feomorphisms of M. In the former case the Lie algebra of the group is the algebra Mg of smooth mappings from M to the Lie algebra gof G. In the latter case the Lie algebra is the algebra Vect M of smooth vector fields on M. However, it turns out that in many applications to field theory and statistical physics one must deal with certain extensions of the above mentioned Lie algebras. In the simplest case M is the unit circle SI, G is a simple finite dimensional Lie group and the central extension of Map( SI, g) is an affine Kac-Moody algebra. The highest weight theory of finite dimensional Lie algebras can be extended to the case of an affine Lie algebra. The important point is that Map(Sl, g) can be split to positive and negative Fourier modes and the finite-dimensional piece g corre sponding to the zero mode.
Download or read book Stochastic Processes Physics and Geometry New Interplays II written by Sergio Albeverio and published by American Mathematical Soc.. This book was released on 2000 with total page 650 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume and Stochastic Processes, Physics and Geometry: New Interplays I present state-of-the-art research currently unfolding at the interface between mathematics and physics. Included are select articles from the international conference held in Leipzig (Germany) in honor of Sergio Albeverio's sixtieth birthday. The theme of the conference, "Infinite Dimensional (Stochastic) Analysis and Quantum Physics", was chosen to reflect Albeverio's wide-ranging scientific interests. The articles in these books reflect that broad range of interests and provide a detailed overview highlighting the deep interplay among stochastic processes, mathematical physics, and geometry. The contributions are written by internationally recognized experts in the fields of stochastic analysis, linear and nonlinear (deterministic and stochastic) PDEs, infinite dimensional analysis, functional analysis, commutative and noncommutative probability theory, integrable systems, quantum and statistical mechanics, geometric quantization, and neural networks. Also included are applications in biology and other areas. Most of the contributions are high-level research papers. However, there are also some overviews on topics of general interest. The articles selected for publication in these volumes were specifically chosen to introduce readers to advanced topics, to emphasize interdisciplinary connections, and to stress future research directions. Volume I contains contributions from invited speakers; Volume II contains additional contributed papers. Members of the Canadian Mathematical Society may order at the AMS member price.
Download or read book Quantum Fields and Quantum Space Time written by Gerard 't Hooft and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 1996 NATO Advanced Study Institute (ASI) followed the international tradi tion of the schools held in Cargese in 1976, 1979, 1983, 1987 and 1991. Impressive progress in quantum field theory had been made since the last school in 1991. Much of it is connected with the interplay of quantum theory and the structure of space time, including canonical gravity, black holes, string theory, application of noncommutative differential geometry, and quantum symmetries. In addition there had recently been important advances in quantum field theory which exploited the electromagnetic duality in certain supersymmetric gauge theories. The school reviewed these developments. Lectures were included to explain how the "monopole equations" of Seiberg and Witten can be exploited. They were presented by E. Rabinovici, and supplemented by an extra 2 hours of lectures by A. Bilal. Both the N = 1 and N = 2 supersymmetric Yang Mills theory and resulting equivalences between field theories with different gauge group were discussed in detail. There are several roads to quantum space time and a unification of quantum theory and gravity. There is increasing evidence that canonical gravity might be a consistent theory after all when treated in. a nonperturbative fashion. H. Nicolai presented a series of introductory lectures. He dealt in detail with an integrable model which is obtained by dimensional reduction in the presence of a symmetry.
Download or read book Locally Conformal K hler Geometry written by Sorin Dragomir and published by Springer Science & Business Media. This book was released on 1998 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: . E C, 0 1'1 1, and n E Z, n ~ 2. Let~.. be the O-dimensional Lie n group generated by the transformation z ~ >.z, z E C - {a}. Then (cf.
Download or read book Collection of Papers on Geometry Analysis and Mathematical Physics written by Daqian Li and published by World Scientific. This book was released on 1997 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is published in honor of Professor Gu Chaohao, a renowned mathematician and member of the Chinese Academy of Sciences, on the occasion of his 70th birthday and his 50th year of educational work. The subjects covered by this collection are closely related to differential geometry, partial differential equations and mathematical physics ? the major areas in which Professor Gu has received notable achievements. Many distinguished mathematicians all over the world contributed their papers to this collection. This collection also consists of ?Gu Chaohao and I? written by C N Yang, ?The academic career and accomplishment of Professor Gu Chaohao? by T T Li and ?List of publications of Professor Gu Chaohao?.
Download or read book Geometry and Analysis on Manifolds written by Takushiro Ochiai and published by Springer. This book was released on 2015-02-25 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is dedicated to the memory of Shoshichi Kobayashi, and gathers contributions from distinguished researchers working on topics close to his research areas. The book is organized into three parts, with the first part presenting an overview of Professor Shoshichi Kobayashi’s career. This is followed by two expository course lectures (the second part) on recent topics in extremal Kähler metrics and value distribution theory, which will be helpful for graduate students in mathematics interested in new topics in complex geometry and complex analysis. Lastly, the third part of the volume collects authoritative research papers on differential geometry and complex analysis. Professor Shoshichi Kobayashi was a recognized international leader in the areas of differential and complex geometry. He contributed crucial ideas that are still considered fundamental in these fields. The book will be of interest to researchers in the fields of differential geometry, complex geometry, and several complex variables geometry, as well as to graduate students in mathematics.
