Yang-Mills measure on compact surfaces
著者
書誌事項
Yang-Mills measure on compact surfaces
（Memoirs of the American Mathematical Society, no. 790）
American Mathematical Society, 2003
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注記
"November 2003, volume 166, number 790 (end of volume)."
Includes bibliographical references (p. 121-122)
内容説明・目次
内容説明
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.
目次
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.
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