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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.
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Book Description Amer Mathematical Society, 2003. Condition: Good. Shows some signs of wear, and may have some markings on the inside. Seller Inventory # GRP104732932
Book Description Amer Mathematical Society, 2003. Paperback. Condition: Used: Good. Seller Inventory # SONG0821834290