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Yang-Mills Measure on Compact Surfaces
Thierry Lévy
出版American Mathematical Soc., 2003
主題Mathematics / AppliedMathematics / CalculusScience / Physics / Quantum TheoryScience / Waves & Wave Mechanics
ISBN08218342909780821834299
URLhttp://books.google.com.hk/books?id=ytfUCQAAQBAJ&hl=&source=gbs_api
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註釋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.