منابع مشابه
Yang-Mills Measure on Compact Surfaces
We construct and study the Yang-Mills measure in two dimensions. According to the informal description given by the physicists, it is a probability measure on the space of connections modulo gauge transformations on a principal bundle with compact structure group. We are interested in the case where the base space of this bundle is a compact orientable surface. The construction of the measure i...
متن کاملA large deviation principle for the Yang-Mills measure
We prove the first mathematical result relating the Yang-Mills measure on a compact surface and the Yang-Mills energy. We show that, at the small volume limit, the scaled Yang-Mills measures satisfy a large deviation principle with the Yang-Mills energy as rate function. This gives some rigorous content to the informal description of the Yang-Mills measure as the Gibbs measure of the Yang-Mills...
متن کاملYang–Mills measure and the master field on the sphere∗
Here is a first version of a study of the Yang–Mills measure on the sphere with structure group of large dimension. We focus in this article on unitary structure groups. We show that the Wilson loops converge in probability towards a deterministic field, called master field. As a corollary, we obtain that the Brownian loop in unitary matrices converges in non-commutative distribution as the dim...
متن کاملThe Volume Measure for Flat Connections as Limit of the Yang–Mills Measure
We prove that integration over the moduli space of flat connections can be obtained as a limit of integration with respect to the Yang– Mills measure defined in terms of the heat kernel for the gauge group. In doing this we also give a rigorous proof of Witten’s formula for the symplectic volume of the moduli space of flat connections. Our proof uses an elementary identity connecting determinan...
متن کاملOn the invariant measure for the Yang-Mills configuration space in (3+1) dimensions
We consider a gauge-invariant Hamiltonian analysis for Yang-Mills theories in three spatial dimensions. The gauge potentials are parametrized in terms of a matrix variable which facilitates the elimination of the gauge degrees of freedom. We develop an approximate calculation of the volume element on the gauge-invariant configuration space, pointing out features related to dimensional transmuta...
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 1992
ISSN: 0022-1236
DOI: 10.1016/0022-1236(92)90025-e