Kahler Geometry of Loop Spaces
Author: Armen G. Sergeev
Publisher:
Published: 2008
Total Pages: 226
ISBN-13:
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Kahler geometry of loop spaces
Author: Armen Sergeev
Publisher: Mathematical Society Of Japan Memoirs
Published: 2010-05
Total Pages: 212
ISBN-13: 9784931469600
DOWNLOAD EBOOKIn 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
Loop Spaces, Characteristic Classes and Geometric Quantization
Author: Jean-Luc Brylinski
Publisher: Springer Science & Business Media
Published: 2009-12-30
Total Pages: 318
ISBN-13: 0817647317
DOWNLOAD EBOOKThis 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.
Topological Geometrodynamics
Author: Matti Pitkanen
Publisher: Bentham Science Publishers
Published: 2016-03-03
Total Pages: 1235
ISBN-13: 1681081792
DOWNLOAD EBOOKTopological 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.
Mathematical Analysis of Random Phenomena
Author: Ana Bela Cruzeiro
Publisher: World Scientific
Published: 2007
Total Pages: 241
ISBN-13: 9812706038
DOWNLOAD EBOOKThis 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.
Complex Differential Geometry and Supermanifolds in Strings and Fields
Author: Petrus J.M. Bongaarts
Publisher: Springer
Published: 1988-10-12
Total Pages: 268
ISBN-13:
DOWNLOAD EBOOKThis 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.
Complex Monge–Ampère Equations and Geodesics in the Space of Kähler Metrics
Author: Vincent Guedj
Publisher: Springer Science & Business Media
Published: 2012-01-06
Total Pages: 315
ISBN-13: 3642236685
DOWNLOAD EBOOKThe 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.
Infinite Dimensional Algebras and Quantum Integrable Systems
Author: Petr P. Kulish
Publisher: Springer Science & Business Media
Published: 2006-01-17
Total Pages: 266
ISBN-13: 3764373415
DOWNLOAD EBOOKThis 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.
Collection of Papers on Geometry, Analysis and Mathematical Physics
Author: Daqian Li
Publisher: World Scientific
Published: 1997
Total Pages: 196
ISBN-13: 9789810230241
DOWNLOAD EBOOKThis 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?.
Differential Geometry: Geometry in Mathematical Physics and Related Topics
Author: Robert Everist Greene
Publisher: American Mathematical Soc.
Published: 1993
Total Pages: 681
ISBN-13: 0821814958
DOWNLOAD EBOOKThe 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
