| eBook 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 |
| eBook 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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Book DetailsMemoirs of the American Mathematical SocietyVolume: 166; 2003; 122 ppMSC: 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.
ReadershipGraduate students and research mathematicians interested in geometry, topology, and analysis.
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Table of Contents
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Chapters
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1. Discrete Yang-Mills measure
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2. Continuous Yang-Mills measure
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3. Abelian gauge theory
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4. Small scale structure in the semi-simple case
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5. Surgery of the Yang-Mills measure
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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.
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
