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Yang-Mills Measure on Compact Surfaces

2003 Mathematics
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Release : 2003
Genre : Mathematics
Kind : eBook
Book Rating : 290/5 ( reviews)

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Book Synopsis Yang-Mills Measure on Compact Surfaces by : Thierry Lévy

Download or read book Yang-Mills Measure on Compact Surfaces written by Thierry Lévy. This book was released on 2003. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Yang-Mills Measure on Compact Surfaces

2014-09-11 Quantum field theory
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Release : 2014-09-11
Genre : Quantum field theory
Kind : eBook
Book Rating : 881/5 ( reviews)

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Book Synopsis Yang-Mills Measure on Compact Surfaces by : Thierry Lévy

Download or read book Yang-Mills Measure on Compact Surfaces written by Thierry Lévy. This book was released on 2014-09-11. Available in PDF, EPUB and Kindle. Book excerpt: Discrete Yang-Mills measure Continuous Yang-Mills measure Abelian gauge theory Small scale structure in the semi-simple case Surgery of the Yang-Mills measure Bibliography.

Gauge Theory on Compact Surfaces

1997 Mathematics
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Release : 1997
Genre : Mathematics
Kind : eBook
Book Rating : 847/5 ( reviews)

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Book Synopsis Gauge Theory on Compact Surfaces by : Ambar Sengupta

Download or read book Gauge Theory on Compact Surfaces written by Ambar Sengupta. This book was released on 1997. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Stochastic Geometric Mechanics

2017-11-17 Mathematics
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Release : 2017-11-17
Genre : Mathematics
Kind : eBook
Book Rating : 534/5 ( reviews)

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Book Synopsis Stochastic Geometric Mechanics by : Sergio Albeverio

Download or read book Stochastic Geometric Mechanics written by Sergio Albeverio. This book was released on 2017-11-17. Available in PDF, EPUB and Kindle. Book excerpt: Collecting together contributed lectures and mini-courses, this book details the research presented in a special semester titled “Geometric mechanics – variational and stochastic methods” run in the first half of 2015 at the Centre Interfacultaire Bernoulli (CIB) of the Ecole Polytechnique Fédérale de Lausanne. The aim of the semester was to develop a common language needed to handle the wide variety of problems and phenomena occurring in stochastic geometric mechanics. It gathered mathematicians and scientists from several different areas of mathematics (from analysis, probability, numerical analysis and statistics, to algebra, geometry, topology, representation theory, and dynamical systems theory) and also areas of mathematical physics, control theory, robotics, and the life sciences, with the aim of developing the new research area in a concentrated joint effort, both from the theoretical and applied points of view. The lectures were given by leading specialists in different areas of mathematics and its applications, building bridges among the various communities involved and working jointly on developing the envisaged new interdisciplinary subject of stochastic geometric mechanics.

Chern-Simons Gauge Theory: 20 Years After

2011 Mathematics
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Release : 2011
Genre : Mathematics
Kind : eBook
Book Rating : 538/5 ( reviews)

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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. This book was released on 2011. 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.

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