Yang-Mills Measure on Compact Surfaces

By Thierry Lévy

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.

• Format: Paperback
• Language: English
• ISBN: 0821834290
• ISBN13: 9780821834299
• Release Date: November 2003
• Publisher: Amer Mathematical Society
• Length: 122 Pages
• Weight: 0.65 lbs.
• Dimensions: 9.8" x 0.3" x 7.0"