Gauge Theory On Compact Surfaces
Download Gauge Theory On Compact Surfaces full books in PDF, epub, and Kindle. Read online free Gauge Theory On Compact Surfaces ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
| Author | : Ambar Sengupta |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 98 |
| Release | : 1997 |
| Genre | : Mathematics |
| ISBN | : 0821804847 |
In this paper we develop a concrete description of connections on principal bundles, possibly non-trivial, over compact surfaces and use this description to construct the Yang-Mills measure which underlies the Euclidean quantum theory of gauge fields, involving compact gauge groups, on compact connected two-dimensional Riemannian manifolds (possibly with boundary). Using this measure we compute expectation values of important random variables, the Wilson loops variables, corresponding to a broad class of configurations of loops on the surface.
| Author | : W. Barth |
| Publisher | : Springer |
| Total Pages | : 439 |
| Release | : 2015-05-22 |
| Genre | : Mathematics |
| ISBN | : 3642577393 |
In the 19 years which passed since the first edition was published, several important developments have taken place in the theory of surfaces. The most sensational one concerns the differentiable structure of surfaces. Twenty years ago very little was known about differentiable structures on 4-manifolds, but in the meantime Donaldson on the one hand and Seiberg and Witten on the other hand, have found, inspired by gauge theory, totally new invariants. Strikingly, together with the theory explained in this book these invariants yield a wealth of new results about the differentiable structure of algebraic surfaces. Other developments include the systematic use of nef-divisors (in ac cordance with the progress made in the classification of higher dimensional algebraic varieties), a better understanding of Kahler structures on surfaces, and Reider's new approach to adjoint mappings. All these developments have been incorporated in the present edition, though the Donaldson and Seiberg-Witten theory only by way of examples. Of course we use the opportunity to correct some minor mistakes, which we ether have discovered ourselves or which were communicated to us by careful readers to whom we are much obliged.
| Author | : Thierry Lévy |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 144 |
| Release | : 2003 |
| Genre | : Mathematics |
| ISBN | : 0821834290 |
In this memoir we present a new construction and new properties of the Yang-Mills measure in two dimensions. This measure was first introduced for the needs of quantum field theory and can be described informally as a probability measure on the space of connections modulo gauge transformations on a principal bundle. We consider the case of a bundle over a compact orientable surface. Our construction is based on the discrete Yang-Mills theory of which we give a full acount. We are able to take its continuum limit and to define a pathwise multiplicative process of random holonomy indexed by the class of piecewise embedded loops. We study in detail the links between this process and a white noise and prove a result of asymptotic independence in the case of a semi-simple structure group. We also investigate global Markovian properties of the measure related to the surgery of surfaces.
| Author | : Kenji Ueno |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 178 |
| Release | : 2008 |
| Genre | : Mathematics |
| ISBN | : 0821840886 |
This book presents a systematic approach to conformal field theory with gauge symmetry from the point of view of complex algebraic geometry. After presenting the basic facts of the theory of compact Riemann surfaces and the representation theory of affine Lie algebras in Chapters 1 and 2, conformal blocks for pointed Riemann surfaces with coordinates are constructed in Chapter 3. In Chapter 4 the sheaf of conformal blocks associated to a family of pointed Riemann surfaces withcoordinates is constructed, and in Chapter 5 it is shown that this sheaf supports a projective flat connection-one of the most important facts of conformal field theory. Chapter 6 is devoted to the study of the detailed structure of the conformal field theory over $\mathbb{P}1$.Recently it was shown that modular functors can be constructed from conformal field theory, giving an interesting relationship between algebraic geometry and topological quantum field theory. This book provides a timely introduction to an intensively studied topic of conformal field theory with gauge symmetry by a leading algebraic geometer, and includes all the necessary techniques and results that are used to construct the modular functor.
| Author | : Francesco Guerra |
| Publisher | : World Scientific |
| Total Pages | : 474 |
| Release | : 1992-07-17 |
| Genre | : |
| ISBN | : 9814555061 |
The aim of the Workshop was to bring together scientists involved in approaching topical problems in mathematical physics by probabilistic methods. Main topics included: Kinetic Theory, Random Systems and Stochastic Mechanics, Nonequilibrium Statistical Mechanics, and Quantum Theory. The book will be an important source for researchers and graduate students in mathematical physics looking for an up to date survey of the subject.
| Author | : Brian Hatfield |
| Publisher | : CRC Press |
| Total Pages | : 753 |
| Release | : 2018-03-09 |
| Genre | : Science |
| ISBN | : 0429961782 |
First Published in 2018. The emphasis of the book is calculational, and most computations are presented in step-by-step detail. The book is unique in that it develops all three representations of quantum field theory (operator, functional Schr dinger, and path integral) for point particles and strings. In many cases, identical results are worked out in each representation to emphasize the representation-independent structures of quantum field theory
| Author | : Nicholas P. Landsman |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 547 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 146121680X |
This monograph draws on two traditions: the algebraic formulation of quantum mechanics as well as quantum field theory, and the geometric theory of classical mechanics. These are combined in a unified treatment of the theory of Poisson algebras of observables and pure state spaces with a transition probability, which leads on to a discussion of the theory of quantization and the classical limit from this perspective. A prototype of quantization comes from the analogy between the C*- algebra of a Lie groupoid and the Poisson algebra of the corresponding Lie algebroid. The parallel between reduction of symplectic manifolds in classical mechanics and induced representations of groups and C*- algebras in quantum mechanics plays an equally important role. Examples from physics include constrained quantization, curved spaces, magnetic monopoles, gauge theories, massless particles, and $theta$- vacua. Accessible to mathematicians with some prior knowledge of classical and quantum mechanics, and to mathematical physicists and theoretical physicists with some background in functional analysis.
| Author | : S. K. Donaldson |
| Publisher | : Oxford University Press |
| Total Pages | : 464 |
| Release | : 1997 |
| Genre | : Language Arts & Disciplines |
| ISBN | : 9780198502692 |
This text provides an accessible account to the modern study of the geometry of four-manifolds. Prerequisites are a firm grounding in differential topology and geometry, as may be gained from the first year of a graduate course.
| Author | : Jurg Frohlich |
| Publisher | : World Scientific |
| Total Pages | : 855 |
| Release | : 1992-04-29 |
| Genre | : |
| ISBN | : 9814506567 |
Compiled to illustrate the recent history of Quantum Field Theory and its trends, this collection of selected reprints by Jürg Fröhlich, a leading theoretician in the field, is a comprehensive guide of the more mathematical aspects of the subject. Results and methods of the past fifteen years are reviewed. The analytical methods employed are non-perturbative and, for the larger part, mathematically rigorous. Most articles are review articles surveying certain important developments in quantum field theory and guiding the reader towards the original literature.The volume begins with a comprehensive introduction by Jürg Fröhlich.The theory of phase transitions and continuous symmetry breaking is reviewed in the first section. The second section discusses the non-perturbative quantization of topological solitons. The third section is devoted to the study of gauge fields. A paper on the triviality of λϖ4 — theory in four and more dimensions is found in the fourth section, while the fifth contains two articles on “random geometry”. The sixth and final part addresses topics in low-dimensional quantum field theory, including braid statistics, two-dimensional conformal field theory and an application to condensed matter theory.
| Author | : Ana Isabel Cardoso |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 455 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 9401102198 |
Proceedings of the NATO Advanced Study Institute, Funchal, Madeira, Portugal, August 6--19, 1993
