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Yang-Mills Measure on Compact Surfaces
 
Thierry Lévy :  Université de Strasbourg, Strasbourg, France
Front Cover for Yang-Mills Measure on Compact Surfaces
Available Formats:
Electronic ISBN: 978-1-4704-0388-1
Product Code: MEMO/166/790.E
List Price: $62.00
MAA Member Price: $55.80
AMS Member Price: $37.20
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Front Cover for Yang-Mills Measure on Compact Surfaces
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  • Front Cover for Yang-Mills Measure on Compact Surfaces
  • Back Cover for Yang-Mills Measure on Compact Surfaces
Yang-Mills Measure on Compact Surfaces
Thierry Lévy :  Université de Strasbourg, Strasbourg, France
Available Formats:
Electronic ISBN:  978-1-4704-0388-1
Product Code:  MEMO/166/790.E
List Price: $62.00
MAA Member Price: $55.80
AMS Member Price: $37.20
Add to cart
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 166; 2003; 122 pp
    MSC: Primary 58; 81; 60;

    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.
    Readership

    Graduate students and research mathematicians interested in geometry, topology, and analysis.
  • Table of Contents
     
     
    • Chapters
    • 1. Discrete Yang-Mills measure
    • 2. Continuous Yang-Mills measure
    • 3. Abelian gauge theory
    • 4. Small scale structure in the semi-simple case
    • 5. Surgery of the Yang-Mills measure
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Memoirs of the American Mathematical Society
Volume: 166; 2003; 122 pp
MSC: Primary 58; 81; 60;

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.
Readership

Graduate students and research mathematicians interested in geometry, topology, and analysis.
  • Chapters
  • 1. Discrete Yang-Mills measure
  • 2. Continuous Yang-Mills measure
  • 3. Abelian gauge theory
  • 4. Small scale structure in the semi-simple case
  • 5. Surgery of the Yang-Mills measure
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